diff --git a/babel.config.js b/babel.config.js
deleted file mode 100644
index 0adade1..0000000
--- a/babel.config.js
+++ /dev/null
@@ -1,3 +0,0 @@
-module.exports = {
-    presets: [require.resolve('@docusaurus/core/lib/babel/preset')],
-};
diff --git a/docs/informatik/informatik.mdx b/docs/informatik/informatik.mdx
index 9ff6f66..10f92c3 100644
--- a/docs/informatik/informatik.mdx
+++ b/docs/informatik/informatik.mdx
@@ -5,7 +5,7 @@ sidebar_position: 1
 ---
 
 # Informatik - eine Einführung
-## Drucker, Windows und Programmieren?
+## Drucker, Windows und Programmieren? {/* #drucker-windows-und-programmieren */}
 Am Anfang möchte ich mich ein wenig mit der Frage beschäftigen, was die Informatik eigentlich ist.
 
 Einige würden sagen, es geht darum, wie man *Windows*, *Office*-Programme oder eine andere Software bedient.
@@ -14,12 +14,12 @@ Aber das ist zu leicht gedacht, wenn nicht sogar völlig inkorrekt.
 Auch ist nicht überall Informatik drin, wo Informatik draufsteht: 
 Informatik-Schulunterricht oder *Fachinformatiker*-Ausbildung (das meine ich überhaupt nicht böse oder entwertend!).
 
-## Informatik = Computer?
+## Informatik = Computer? {/* #informatik--computer */}
 Eine der häufigsten Antworten auf die Frage, was Informatik eigentlich ist, 
 hört man, dass die was mit Computer zu tun haben. 
 Das ist nicht ganz falsch, aber bei weitem auch nicht ganz richtig. 
 
-### Ein Versuch einer Definition
+### Ein Versuch einer Definition {/* #ein-versuch-einer-definition */}
 Im Folgenden möchte ich ein paar verschiedene Definitionen aufzeigen, die allesamt ähnlich sind.
 
 :::note Informatik
@@ -57,7 +57,7 @@ weshalb ich diese weiter oben erwähnt habe.
 Informatik als Wissenschaft **ist** Mathematik, alles baut darauf auf und aus meiner Sicht ist das gerade der
 essenziellste Teil!
 
-### Informatik = IT?
+### Informatik = IT? {/* #informatik--it */}
 Außerdem hört man häufig, dass Menschen die **IT** mit **Informatik** gleichsetzen, auch das ist nicht ganz korrekt.
 Die Informatik als Wissenschaft streift verschiedenste Themengebiete und andere Wissenschaften, die **Informationstechnik**
 (IT) ist nur eine davon, wenngleich keine unwichtige!
@@ -79,7 +79,7 @@ Folgendes (chaotisches) Schaubild zeigt ein wenig das Zusammenspiel von den Wiss
 
 ![Informatik in Bezug auf andere Wissenschaften und Technikbereiche](/img/informatik/informatik/informatik_it.svg)
 
-## Teilgebiete der Informatik
+## Teilgebiete der Informatik {/* #teilgebiete-der-informatik */}
 Im Folgenden möchte ich die Informatik und ihre Teilgebiete und dessen Bezug zu anderen Wissenschaften oder Techniken etwas genauer vorstellen.
 Bisher habe ich noch keine konkreten Namen genannt, womit sich die Informatik denn genau beschäftigt.
 Folgendes Schaubild liefert einen ersten Überblick:
@@ -89,7 +89,7 @@ Folgendes Schaubild liefert einen ersten Überblick:
 Einige der unten aufgezählten Untersuchungsgebiete lassen sich auch anderen Teilgebieten zuordnen,
 da diese natürlich untereinander enge Verbindungen haben und es sich nicht immer klar abgrenzen lässt.
 
-### Theoretische Informatik
+### Theoretische Informatik {/* #theoretische-informatik */}
 Die theoretische Informatik entstand aus der Mathematik und bildet die theoretische Grundlage aller anderen Teilgebiete.
 
 :::note Theoretische Informatik
@@ -109,7 +109,7 @@ Sie umfasst unter anderem folgende Untersuchungsgebiete:
 - Komplexität (Rechen- und Speicheraufwand)
 - Graphentheorie
 
-### Technische Informatik
+### Technische Informatik {/* #technische-informatik */}
 Die technische Informatik steht eng mit der Elektrotechnik und Nachrichtentechnik in Verbindung und hat tatsächlich etwas mit Computer zu tun.
 
 :::note Technische Informatik
@@ -130,7 +130,7 @@ Sie umfasst unter anderem folgende Untersuchungsgebiete:
 - Hardwareentwurf
 - Eingebettete Systeme
 
-### Praktische Informatik
+### Praktische Informatik {/* #praktische-informatik */}
 Die praktische Informatik beschäftigt sich zum einen mit Programmiersprachen selbst und ihren Eigenschaften, 
 aber auch mit der Softwaretechnik (u.a. Design, Entwurf, Test und Projektmanagement).
 
@@ -148,7 +148,7 @@ Sie umfasst unter anderem folgende Untersuchungsgebiete:
 - Betriebssysteme (eng mit technischer Informatik)
 - Softwareentwicklung
 
-### Angewandte Informatik
+### Angewandte Informatik {/* #angewandte-informatik */}
 Die angewandte Informatik verwendet nun viele Erkenntnisse aus den obigen Teilen und 
 wendet diese in anderen Bereichen und im Alltag an.
 
diff --git a/docs/intro.mdx b/docs/intro.mdx
index c2271d8..19f173b 100644
--- a/docs/intro.mdx
+++ b/docs/intro.mdx
@@ -5,7 +5,7 @@ description: Hallo
 sidebar_position: 1
 ---
 
-## Die Welt der Mathematik ist eine Schöne.
+## Die Welt der Mathematik ist eine Schöne. {/* #die-welt-der-mathematik-ist-eine-schöne */}
 
 **Wieso erwähne ich nur die Mathematik, obwohl es doch noch zwei weitere große Themenkomplexe gibt?**
 
@@ -31,40 +31,39 @@ was die Eingangsfrage beantwortet.
 Doch widmen wir uns der Überschrift:
 > Die Welt der Mathematik ist eine Schöne.
 
-Einige von euch werden nun vielleicht angewidert den Kopf schütteln,
-doch das ist nicht ganz fair.
+Vielleicht wirst du nun angewidert den Kopf schütteln, doch das ist nicht ganz fair.
 Die Mathematik aus der Schule unterscheidet sich von der *höheren Mathematik*, wie sie im Studium gelehrt wird.
-Wer diese höhere Mathematik geschnuppert und ihr eine Chance gegeben hat, der wird vielleicht gefallen an ihr gefunden haben.
+Wer diese höhere Mathematik geschnuppert und ihr eine Chance gegeben hat, der wird vielleicht gefallen an ihr finden.
 
-## Wer bin ich?
-Ich bin ein Mittzwanziger, der unheimlich gerne über die Themen redet und alles davon wissen will, 
-aber eigentlich gar nicht so gut darin ist.
-Ich habe einen *Bachelor of Science* in *angewandter Informatik* und studiere aktuell *angewandte Mathematik*.
+## Wer bin ich? {/* #wer-bin-ich */}
+Ich liebe die Mathematik und Informatik und ich würde gerne viel mehr darüber reden und alles davon wissen.
+Leider bin ich eigentlich gar nicht so gut darin Mathematik und Informatik zu betreiben.
+Ich habe einen *Bachelor of Science* in *Angewandte Informatik* und studiere aktuell nebenberuflich *Praktische Informatik* im Master.
+Vor dem Master habe ich einige Jahre *Angewandte Mathematik* studiert, musste aber leider zwischendrin abbrechen.
 Bevor ich studiert habe, habe ich eine Ausbildung zum *Informations- und Kommunikationstechnischen Assistenten* absolviert.
-Ich fühle mich also in der Mathematik, der Informatik und der Programmierung wohl.
+Beruflich arbeite ich als System- und Netzwerkadministrator in einer Behörde mit Sicherheitsaufgaben.
 
-## Wozu das Ganze hier?
-Ich möchte ein umfangreiches Werk erschaffen, das meine Studieninhalte aufgreift und sowohl komprimiert, als auch erweitert.
+## Wozu das Ganze hier? {/* #wozu-das-ganze-hier */}
+Ich möchte ein Werk erschaffen, das meine Studieninhalte aufgreift und sowohl komprimiert, als auch erweitert.
 Was meine ich damit?
 Ich kann hier nicht alles *ganz penibel* aufschreiben, was in meinen Skripten steht, auch wenn ich mich an diesen orientiere.
 Aber ich ziehe auch andere Quellen als die Skripte meiner Professoren her - Skripte anderer Professoren, Bücher, eigene Erfahrung, etc.
 Dabei versuche ich die Sachverhalte in meinen Worten wiederzugeben - zum Einen, um es selbst besser zu verstehen 
-und zum Anderen, um es euch zugänglicher zu machen.
+und zum Anderen, um es anderen zugänglicher zu machen.
 
 Es geht also darum, mein Wissen hier zu konservieren und an andere weiterzugeben.
 
-## Für wen das Ganze?
+## Für wen das Ganze? {/* #für-wen-das-ganze */}
 Diese Seite richtet sich an jede Person, die Interesse an den Themen hat.
-Das Niveau ist allerdings Hochschulniveau und eignet sich daher nicht unbedingt für Schülerinnen oder Schüler, 
-die gerade für etwas lernen.
-Das sollte euch aber nicht davon abhalten, trotzdem mal reinzulesen, wenn es euch interessiert.
-Vielleicht denkt sich jemand von euch ja, dass das etwas ist, das ihr in Zukunft machen wollt.
-Im *MINT*-Bereich (**M**athematik, **I**nformatik, **N**aturwissenschaft, **T**echnik) gibt es viele Studienabbrecher,
+Primäre Zielgruppe sind aber Hochschulstudierende.
+Das sollte dich aber nicht davon abhalten, trotzdem mal reinzulesen, wenn es dich interessiert.
+Vielleicht denkst du dir ja, dass das etwas ist, das du in Zukunft machen willst.
+Im *MINT*-Bereich (**M**athematik, **I**nformatik, **N**aturwissenschaft, **T**echnik) gibt es einige Studienabbrecher,
 da das alles nicht gerade einfach ist und vielen die essenzielle Mathematik Schwierigkeiten bereitet.
-Doch wir brauchen viele von euch, die ein MINT-Studium absolvieren und vor allem Mädchen und Frauen sind weit unterrepräsentiert.
+Doch wir brauchen viele, die ein MINT-Studium absolvieren und vor allem Frauen sind weit unterrepräsentiert.
 Eine allgemein höhere Diversität im MINT-Bereich ist erstrebens- und wünschenswert.
 
-## Wie verarbeitet ihr das hier?
+## Wie verarbeitest du das hier? {/* #wie-verarbeitest-du-das-hier */}
 Das liegt ganz bei dir.
 Die Unterthemen sind mehr oder weniger chronologisch angeordnet, wie man sie auch im Studium einführt.
 Du kannst also bequem den Programmierteil beginnen, ohne vorher die Mathematik durchgearbeitet zu haben.
@@ -73,13 +72,10 @@ Solltest du schon Vorkenntnisse haben, kannst du natürlich auch ab da einsteige
 zurückblättern kann man immer, falls doch noch was fehlt.
 Auf den Übersichtsseiten der einzelnen Oberthemen findest du hierzu jedoch weitere Informationen.
 
-## Ihr wollt mitmachen oder Fehler melden?
-Das Projekt ist in erster Linie ein Projekt von *mir* für *euch*.
-Falls ihr jedoch Interesse an eine Art Gastbeitrag habt, ihr einen Fehler (Rechtschreibung, Grammatik, Inhaltlich, etc.)
-gefunden oder einen Themenwunsch habt, dann könnt ihr mich gerne unter 
-[niklas.birk@niklas-birk.de](mailto://niklas.birk@niklas-birk.de) erreichen und ich schaue, 
-wie und ob ich euch weiterhelfen kann.
+## Du willst einen Fehler melden? {/* #du-willst-einen-fehler-melden */}
+Falls du du einen Fehler (Rechtschreibung, Grammatik, Inhaltlich, etc.)
+gefunden oder einen Themenwunsch hast, dann kannst du mich gerne unter
+[me@niklas-birk.de](mailto://me@niklas-birk.de) erreichen.
 
-Den Code und die Ressourcen zu dieser Website findet ihr unter [git.niklas-birk.de](https://git.niklas-birk.de/niklas/niklas_birk_blog).
-Da ihr dort jedoch keinen Account anlegen könnt, ist die *Issue*-Funktion nicht verfügbar.
-Alternativ könnt ihr auf [github.com/niklasbirk](https://github.com/niklasbirk/niklas-birk-blog) ein Issue anlegen.
\ No newline at end of file
+Den Code und die Ressourcen zu dieser Website findest du unter [git.niklas-birk.de](https://git.niklas-birk.de/niklas/niklas_birk_blog).
+Da du dort jedoch keinen Account anlegen könnt, ist die *Issue*-Funktion nicht verfügbar.
\ No newline at end of file
diff --git a/docs/mathematik/analysis/analysis.mdx b/docs/mathematik/analysis/analysis.mdx
index 95fde95..0f26dd7 100644
--- a/docs/mathematik/analysis/analysis.mdx
+++ b/docs/mathematik/analysis/analysis.mdx
@@ -4,7 +4,7 @@ tags: [mathematik, mengenlehre, analysis]
 sidebar_position: 1
 ---
 
-## Themen
+## Themen {/* #themen */}
 In diesem Teil möchte ich über folgende Themen sprechen:
 
 1. [Reelle Zahlen](reelle_zahlen)
@@ -23,7 +23,7 @@ In diesem Teil möchte ich über folgende Themen sprechen:
    2. [Uneigentliche- und  Parameterintegrale](integration/integral2)
    3. [Kurvenintegrale](integration/kurvenintegral)
 
-## Über die Analysis
+## Über die Analysis {/* #über-die-analysis */}
 Eine der wichtigsten Teilgebiete der Mathematik bildet die Analysis.
 Sie beschäftigt sich hauptsächlich mit Funktionen in den *reellen* und *komplexen Zahlen*.
 Dabei steht die Untersuchung der Eigenschaften dieser Funktionen im Vordergrund.
diff --git a/docs/mathematik/mathematik.mdx b/docs/mathematik/mathematik.mdx
index 315d335..c417e41 100644
--- a/docs/mathematik/mathematik.mdx
+++ b/docs/mathematik/mathematik.mdx
@@ -5,7 +5,7 @@ sidebar_position: 1
 ---
 
 # Mathematik - eine Einführung
-## Zur Beliebtheit der Mathematik
+## Zur Beliebtheit der Mathematik {/* #zur-beliebtheit-der-mathematik */}
 Mathematik wird als nicht besonders beliebtes Schulfach gesehen.
 Dabei galt es 2010 noch als eines der Lieblingsfächer der Deutschen. [^1]
 Trotzdem scheint es so, als ob die meisten das Fach nicht mögen, wenn man sich so umhört.
@@ -16,7 +16,7 @@ doch diese wäre für den Schulunterricht ungeeignet.
 Lediglich in der gymnasialen Oberstufen werden ein paar wenige Konzepte der höheren Mathematik eingeführt,
 wenngleich nicht mit einer hohen mathematischen Strenge oder Abstraktion.
 
-## Mathematik ist überall
+## Mathematik ist überall {/* #mathematik-ist-überall */}
 Aber Mathematik umgibt uns ständig. Wesentliche Zusammenhänge in der Natur lassen sich durch Mathematik beschreiben.
 Zahlen und das Rechnen mit ihnen ist unser täglich Brot, wenn wir beim Bäcker etwas kaufen.
 Sie ist enorm wichtig für uns Menschen, da viele ingenieurwissenschaftlichen Erkenntnisse auf ihr mit der Physik beruhen.
@@ -32,7 +32,7 @@ Galileo Galilei lebte bis ins 17. Jahrhundert, das war lange bevor die Mathemati
 Die neuzeitliche Mathematik, wie sie heute betrieben wird, entwickelte sich erst im 19. und 20. Jahrhundert.
 Dennoch spielte die Mathematik bereits in der Antike und seit jeher eine wichtige Rolle.
 
-## Mathematik = Rechnen?
+## Mathematik = Rechnen? {/* #mathematik--rechnen */}
 Mathematik entstand aus der Untersuchung von geometrischen Figuren und dem Rechnen mit Zahlen.
 Jedoch hat sie sich weiterentwickelt zu etwas, das mit bloßem Rechnen nicht mehr viel zu tun hat.
 Auch die Geometrie hat sich zu etwas entwickelt, was wir uns so gar nicht mehr vorstellen können.
@@ -48,7 +48,7 @@ Ein wahrer logischer Beweis ist prinzipbedingt endgültig und allgemeingültig w
 Im Vergleich dazu werden naturwissenschaftliche Erkenntnisse durch Experimente bestätigt und müssen durch Experimente 
 auch falsifiziert werden können. Solche Erkenntnisse sind daher vorläufig, das kennt die Mathematik nicht.
 
-### Ein Versuch einer Definition
+### Ein Versuch einer Definition {/* #ein-versuch-einer-definition */}
 Eine gemeinhin anerkannte Definition existiert nicht, aber ein grober Versuch zu beschreiben, 
 was die Mathematik ist oder macht könnte folgendermaßen aussehen: 
 
@@ -60,14 +60,14 @@ auf ihre Eigenschaften und Muster untersucht.[^2]
 
 :::
 
-## Einteilung der Mathematik
-### Reine Mathematik
+## Einteilung der Mathematik {/* #einteilung-der-mathematik */}
+### Reine Mathematik {/* #reine-mathematik */}
 Die reine Mathematik beschäftigt sich vorzugsweise mit der Untersuchung der mathematischen Strukturen und Objekte innerhalb der Mathematik.
 Die Theorien dazu werden ggf. erweitert oder verallgemeinert und neue Verbindungen erkannt.
 Dazu werden neue Definitionen eingeführt.
 Außerdem müssen die Verbindungen mathematisch bewiesen und in mathematischer Strenge als Sätze formuliert werden.
 
-### Angewandte Mathematik
+### Angewandte Mathematik {/* #angewandte-mathematik */}
 In der angewandten Mathematik werden die Erkenntnisse der Mathematik auf reale Probleme in anderen Wissenschaften wie 
 Naturwissenschaften, Informatik und Technik angewandt.
 Hierbei wird das Problem aus dem anderen Bereich mathematisch modelliert.
@@ -88,12 +88,12 @@ Folgende Gebiete kann man zur angewandten Mathematik zählen, die mehr oder weni
 - Wirtschaftsmathematik
 - Theoretische Informatik
 
-## Teilgebiete der Mathematik
+## Teilgebiete der Mathematik {/* #teilgebiete-der-mathematik */}
 Die Mathematik hat viele Teilgebiete.
 Vier davon sind besonders hervorzuheben, da sie für viele andere Teilgebiete die absoluten Grundlagen bereitstellen.
 
-### Fundamentale Gebiete
-#### Logik und Mengenlehre
+### Fundamentale Gebiete {/* #fundamentale-gebiete */}
+#### Logik und Mengenlehre {/* #logik-und-mengenlehre */}
 Die Logik ist nicht nur fundamental in der Mathematik. 
 Auch in der Philosophie und Informatik spielt sie eine entscheidende Rolle.
 
@@ -136,7 +136,7 @@ In u.a. folgende Untersuchungs- und Teilgebiete lässt sich die (mathematische)
   - Mengenoperationen
   - Relationen und Funktionen
 
-#### Algebra
+#### Algebra {/* #algebra */}
 Die Algebra wird in der Schule häufig als das "Rechnen mit Unbekannten" und "Lösen von Gleichungen" eingeführt.
 Die Theorie der Algebra hat sich allerdings weiterentwickelt und abstrahiert.
 
@@ -158,7 +158,7 @@ Folgende Untersuchungs- und Teilgebiete können u.a. der Algebra zugeordnet werd
   - Lineare Gleichungssysteme
   - Affine Geometrie
 
-#### Analysis
+#### Analysis {/* #analysis */}
 Die Analysis ist v.a. für Natur- und Ingenieurwissenschaften relevant.
 Sie beschäftigt sich hauptsächlich mit Funktionen in den *reellen* und *komplexen Zahlen*.
 
@@ -179,7 +179,7 @@ Folgende Untersuchungs- und Teilgebiete können u.a. der Analysis zugeordnet wer
 - Funktionalanalysis (Kombination aus Algebra und Analysis)
 - Differentialgleichungen
 
-#### Topologie
+#### Topologie {/* #topologie */}
 Die Topologie beschäftigt sich mit mathematischen Strukturen, deren Struktur unter stetigen Verformungen erhalten bleiben.
 
 :::note Topologie
@@ -194,8 +194,8 @@ Ebenso Begriffe wie Grenzwerte.
 Als Grundlegende Strukturen werden dabei die *topologischen Räume* eingeführt.
 Ein Spezialfall eines topologischen Raumes ist der *metrische Raum*, welcher auch in der Analysis eine bedeutende Rolle spielt.
 
-### Weitere Teilgebiete
-#### Diskrete Mathematik
+### Weitere Teilgebiete {/* #weitere-teilgebiete */}
+#### Diskrete Mathematik {/* #diskrete-mathematik */}
 Die diskrete Mathematik beschäftigt sich mit diskreten Strukturen, während die Analysis bspw. als *kontinuierlich* beschrieben werden kann.
 Sie spielt v.a. in der Informatik eine wichtige Rolle.
 
@@ -212,7 +212,7 @@ Als Untersuchungs- und Teilgebiete der diskreten Mathematik können folgende auf
 - Kombinatorik
 - Zahlentheorie
 
-#### Numerik
+#### Numerik {/* #numerik */}
 Durch die Erkenntnisse der Numerik lassen sich näherungsweise Lösungen durch Computer berechnen.
 
 :::note Numerische Mathematik
@@ -226,7 +226,7 @@ Wenn ein gegebenes Problem mathematisch zu berechnen sehr aufwändig ist und man
 dann kann es Wert sein, eine numerische Lösung dafür zu finden, die erheblich einfacher ist, 
 ganz unabhängig von Computern (z.B. Überschlagen einer Rechnung im Kopf).
 
-#### Stochastik und Statistik
+#### Stochastik und Statistik {/* #stochastik-und-statistik */}
 In der Mathematik sind Ergebnisse erstmal vorherbestimmt, da z.B. eine Rechnung eben nur ein Ergebnis liefert.
 Es gibt jedoch in der echten Welt auch so etwas wie Zufall.
 Da wir die Mathematik gerne als Beschreibungssprache theoretischer Zusammenhänge verwenden,
@@ -264,7 +264,7 @@ Folgende Untersuchungs- und Teilgebiete der Stochastik und Statistik können gen
   - Induktive Statistik
   - Explorative Statistik
 
-#### Geometrie 
+#### Geometrie {/* #geometrie */}
 Geometrie handelte früher von Punkten und Geraden und Figuren, die man damit erstellen konnte.
 Ganz anschaulich konnte man damit Figuren zeichnen und konstruieren.
 Mittlerweile hat sich die Geometrie zu etwas weiterentwickelt, von dem man gar nicht mehr annehmen würde, dass es Geometrie ist.
@@ -289,7 +289,7 @@ Folgende Untersuchungs- und Teilgebiete der Geometrie können genannt werden:
 - Nichteuklidische Geometrie
 - Differentialgeometrie
 
-#### Zahlentheorie 
+#### Zahlentheorie {/* #zahlentheorie */}
 Die Zahlentheorie beschäftigt sich hauptsächlich mit Zahlen.
 In der *elementaren Zahlentheorie* insbesondere mit den *ganzen Zahlen*.
 Begriffe wie Teilbarkeit kommen aus diesem Teilgebiet, genauer gesagt aus der Arithmetik..
diff --git a/docs/mathematik/mengenlehre/1_logik.mdx b/docs/mathematik/mengenlehre/1_logik.mdx
index 5e4605f..f4a03e1 100644
--- a/docs/mathematik/mengenlehre/1_logik.mdx
+++ b/docs/mathematik/mengenlehre/1_logik.mdx
@@ -17,10 +17,10 @@ Syntax und die Semantik hängen in der Logik durchaus eng zusammen, da sie nach
 In der Mathematik sind die Beweise allerdings informal und eher eine Skizze eines formalen logischen Beweises,
 weshalb die strikte Trennung zwischen Syntax und Semantik nicht immer transparent erscheint.
 
-## Aussagenlogik (PL 0)
+## Aussagenlogik (PL 0) {/* #aussagenlogik-pl-0 */}
 Die *Aussagenlogik* oder auch *Prädikatenlogik 0. Stufe* (*PL0*) beschäftigt sich mit *Aussagen*.
 
-:::note Aussagen
+:::note[Aussagen]
 
 *Aussagen* sind Sachverhalte in sprachlicher Form, die in der objektiven Realität vorliegen oder denkbar sind.
 
@@ -29,7 +29,7 @@ Die *Aussagenlogik* oder auch *Prädikatenlogik 0. Stufe* (*PL0*) beschäftigt s
 Diese Definition wirkt etwas sperrig.
 Eine andere Definition wäre:
 
-:::note Aussagen
+:::note[Aussagen]
 
 Eine *Aussage* ist ein sprachliches Gebilde, dem eindeutig ein
 *Wahrheitswert* (*wahr* oder *falsch*) zugeordnet werden kann.
@@ -40,7 +40,7 @@ Diese Definition verknüpft allerdings schon ein bisschen die Syntax (sprachlich
 Sowohl die Syntax, als auch die Semantik werden nachfolgend gesondert eingeführt.
 Nur wenden wir uns dann nicht mehr dem Begriff Aussage selbst zu, sondern nutzen Variablen.
 
-#### Beispiele
+#### Beispiele {/* #beispiele */}
 Folgendes sind Beispiele für Aussagen:
 - "Berlin ist die Hauptstadt von Deutschland"
 - "Kein Auto ist Minzgrün"
@@ -54,10 +54,10 @@ Die anderen Beiden nutzen eine *formale Sprache*.
 Solche Formeln und andere Schreibweisen mit Symbolen können eine formale Sprache bilden.
 Formale Sprachen werden im Teil [Informatik](/docs/informatik) näher behandelt.
 
-### Syntax
+### Syntax {/* #syntax */}
 Aussagenlogische *Formeln* beinhalten verschiedene Symbole und werden rekursiv definiert:
 
-:::note Aussagenlogische Formeln
+:::note[Aussagenlogische Formeln]
 
 Sei $O = \{ \neg, \wedge, \vee, \rightarrow, \leftrightarrow, (, ) \}$ die Menge der *logischen Operatoren* (*Junktoren*)
 und $\Sigma$ eine Menge von Symbolen, die *Aussagevariablen* genannt werden.
@@ -82,7 +82,7 @@ Es sind auch andere Symbole in Verwendung, je nach Person oder je nach Wissensch
 
 Die Junktoren haben einen Namen und eine Sprechweise:
 
-:::note Name und Sprechweise der Junktoren
+:::note[Name und Sprechweise der Junktoren]
 
 $$
 \begin{align*}
@@ -102,10 +102,10 @@ Bisher war es nur Syntax, d.h. rein syntaktische Gebilde ohne Bedeutung.
 Einfach eine korrekte Aneinanderreihung von Symbolen.
 Auch $w$ und $f$ sind erstmal nur Symbole, die allerdings wenig überraschend mit der den Worten entsprechenden Semantik belegt werden.
 
-### Semantik
+### Semantik {/* #semantik */}
 In der Aussagenlogik gilt das *Zweiwertigkeitsprinzip*:
 
-:::note Zweiwertigkeitsprinzip
+:::note[Zweiwertigkeitsprinzip]
 
 Alle Aussagen sind entweder *wahr* ($w$ oder $1$) oder *falsch* ($f$ oder $0$)
 
@@ -121,7 +121,7 @@ Aber nach welchen Regeln soll das $\wedge$, also das *und*, behandelt werden?
 
 Dafür müssen wir diesen syntaktischen Symbolen nun eine Bedeutung mittels einer Wahrheitstabelle eine Semantik geben.
 
-:::note Semantik der Junktoren
+:::note[Semantik der Junktoren]
 
 $$
 \begin{array}{c|c||c|c|c|c|c|c}
@@ -141,7 +141,7 @@ Die Priorität der Junktoren in absteigender Reihenfolge: $\neg, \wedge, \vee, \
 
 Eine Zeile dieser Wahrheitstabelle nennt man auch *Interpretation* oder *Belegung*.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-1 */}
 Wählen wir folgende Aussagen $A = "3 < 5"$ und $B = "3 + 2 = 1"$.
 $A$ ist eine wahre Aussage, während $B$ eine falsche Aussage ist.
 Wir bilden nun die neue Aussage $A \wedge B$.
@@ -161,7 +161,7 @@ nie was Falsches folgern dürfen, aber aus etwas Falschem stets was Wahres:
 - $2^2 = 4 \rightarrow 1+1=1 \qquad\;$ ist falsch
 - $1+1=1 \rightarrow 2+2=4 \quad$ ist wahr
 
-#### Weitere Anmerkungen
+#### Weitere Anmerkungen {/* #weitere-anmerkungen */}
 Bei $\vee$ (gesprochen *oder*) ist anzumerken, dass es sich um ein *Inklusiv-Oder* handelt, d.h. die Gesamtaussage ist genau dann wahr,
 wenn mindestens eine Teilaussage wahr ist.
 Das Inklusiv-Oder ist wie ein "Milch *oder* Zucker" beim Kaffee zu verstehen - man kann auch beides nehmen.
@@ -172,14 +172,14 @@ Die Antivalenz ist auch ein wichtiger Junktor, der hier aber nicht näher eingef
 Die Implikation bereitet vielen am Anfang Bauchschmerzen, da sie dem umgangssprachlichen "wenn ..., dann ..." auf den ersten Blick nicht vollkommen entspricht.
 Hierfür findet man im Web viele weitere Erklärungen und Beispiele, die vielleicht Abhilfe schaffen können.
 
-### Klassifikation von Formeln
-:::note Modell
+### Klassifikation von Formeln {/* #klassifikation-von-formeln */}
+:::note[Modell]
 
 Jede Belegung, unter der die Formel wahr wird nennen wir ein *Modell* der Formel.
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-2 */}
 $$
 \begin{array}{c||c|c||c}
      & A & B & F = (A \wedge B) \rightarrow B\\
@@ -207,7 +207,7 @@ Solche Formeln haben einen bestimmten Namen, der in der nächsten Definition ein
 
 Wir können Formeln nun anhand ihrer Modelle in verschiedene Klassen einteilen:
 
-:::note Klassifikation von Formeln
+:::note[Klassifikation von Formeln]
 
 Falls die Formel mindestens ein Modell hat, nennen wir sie *erfüllbar*.
 
@@ -219,7 +219,7 @@ Man nennt so eine Formel auch *Kontradiktion* oder *Widerspruch*.
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-3 */}
 Oben haben wir bereits eine Tautologie gesehen.
 Eine weitere wäre:
 $$
@@ -246,18 +246,18 @@ Diese Formel nennt man auch *Widerspruch*.
 Es kann $A$ *und* $\neg A$ nie gleichzeitig gelten.
 Wenn also bspw. jemand behauptet "Ich wohne in Berlin", er aber gleichzeitig sagt "Ich wohne nicht in Berlin", dann widerspricht er sich ja selbst.
 
-### Semantische Äquivalenz
+### Semantische Äquivalenz {/* #semantische-äquivalenz */}
 Wenn wir über verschiedene Formeln reden und bestimmen wollen, ob diese Formeln das gleiche Aussagen,
 dann ist das die Frage nach der *semantischen Äquivalenz*.
 
-:::note Semantische Äquivalenz
+:::note[Semantische Äquivalenz]
 
 Zwei Formeln $F$ und $G$ heißen *semantisch äquivalent*, wenn sie die gleichen Modelle haben.
 Man schreibt $F \equiv P$.
 
 :::
 
-#### Beispiel
+#### Beispiel {/* #beispiel */}
 $$
 \begin{array}{c|c||c|c}
     A & B & A \rightarrow B & \neg B \rightarrow \neg A\\
@@ -275,7 +275,7 @@ schonmal mit der objektsprachlichen *syntaktischen Äquivalenz* verknüpft und d
 Es gibt einen wichtigen Zusammenhang zwischen der objektsprachlichen *syntaktischen Äquivalenz*
 und der metasprachlichen *semantischen Äquivalenz*:
 
-:::info Semantische und syntaktische Äquivalenz
+:::info[Semantische und syntaktische Äquivalenz]
 
 Zwei Formeln $F$ und $P$ heißen *semantisch äquivalent*, genau dann, wenn $F \leftrightarrow P$ eine Tautologie ist.
 
@@ -284,7 +284,7 @@ Zwei Formeln $F$ und $P$ heißen *semantisch äquivalent*, genau dann, wenn $F \
 Es gibt ein paar wichtige semantische Äquivalenzen, die uns auch beim *Rechnen* oder *Umformen* von Formeln helfen.
 Die tatsächliche semantische Äquivalenz lässt sich leicht durch aufstellen einer Wertetabelle ermitteln und ist eine gute Übung.
 
-:::tip Wichtige semantische Äquivalenzen
+:::tip[Wichtige semantische Äquivalenzen]
 
 1. $$
     \begin{align*}
@@ -427,7 +427,7 @@ Die tatsächliche semantische Äquivalenz lässt sich leicht durch aufstellen ei
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-4 */}
 Im folgenden Beispiel wird eine Formel durch obige Äquivalenzen in eine äquivalente Formel umgeformt.
 Die verwendete Äquivalenz wird entsprechend der Nummerierung oben angegeben, damit es besser nachvollziehbar ist, was umgeformt wurde.
 $$
@@ -452,17 +452,17 @@ Das Umformen von Gleichungen in der Schule ist übrigens ähnlich.
 Vielleicht hat dein Mathelehrer mal das Wort "*Äquivalenzumformung*" dafür verwendet.
 Es wird so umgeformt, dass sich der Wahrheitswert der Gleichung nicht ändert.
 
-## Prädikatenlogik (PL 1)
+## Prädikatenlogik (PL 1) {/* #prädikatenlogik-pl-1 */}
 Die Aussagenlogik allein reicht leider nicht aus, um viele Problemstellungen in der Mathematik vernünftig zu formulieren.
 
-:::note Variable
+:::note[Variable]
 
 Sei $G$ ein Grundbereich von Objekten.
 Für eine *Variable* $x$ über $G$ kann ein Objekt aus $G$ eingesetzt werden.
 
 :::
 
-:::note Aussagenform
+:::note[Aussagenform]
 
 Eine *Aussagenform* $H$ über $G$ ist ein schriftsprachliches Gebilde mit mindestens einer Variable.
 Durch Einsetzen von Objekten aus $G$ **für alle** Variablen wird $H$ zu einer Aussage.
@@ -475,7 +475,7 @@ Aussagenformen wurden bereits in der [Aussagenlogik](#syntax)) oben eingeführt,
 
 Das Zusammensetzen von Aussagen(-formen) mit den entsprechenden Junktoren ist analog zur Aussagenlogik.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-5 */}
 Sei $G = \mathbb{N}$ Grundbereich und $A(n) \coloneqq ``n + 1 = 3''$ Aussagenform.
 Durch Ersetzen der Variable $n$ durch ein Objekt aus $G$, hier also einer natürlichen Zahl, wird $A(x)$ zu einer Aussage:
 - Für $n = 1$ ist $A(1) \coloneqq ``1 + 1 = 3''$ eine falsche Aussage.
@@ -488,7 +488,7 @@ während $Mensch(Grumpy Cat)$, sprich "Grumpy Cat ist ein Mensch" eine falsche A
 
 Doch in der Prädikatenlogik gibt es noch mehr, was diese ausmacht:
 
-:::note Quantifizierung
+:::note[Quantifizierung]
 
 Quantoren:
 - Allquantor: $\forall x$ - sprich: "Für alle $x$ aus $G$"
@@ -506,7 +506,7 @@ Nicht gebundene Variablen heißen *frei*.
 Eine Aussagenform wurde erst zu einer Aussage, wenn wir die Variablen durch ein konkretes Objekt aus $G$ ersetzt haben.
 Durch ein Quantor ist eine Aussagenform direkt eine Aussage:
 
-#### Beispiele
+#### Beispiele {/* #beispiele-6 */}
 Sei $G = \mathbb{N}$ Grundbereich und $H(x) \coloneqq ``x + 1 = 3''$ Aussagenform.
 Durch Quantifizierung entstehen folgende Aussagen:
 - $\forall x (x + 1 = 3)$ - "Für alle $x$ aus $G$ gilt $x + 1 = 3$" ist eine falsche Aussage.
diff --git a/docs/mathematik/mengenlehre/2_mengen.mdx b/docs/mathematik/mengenlehre/2_mengen.mdx
index 93dcfb5..83ba8eb 100644
--- a/docs/mathematik/mengenlehre/2_mengen.mdx
+++ b/docs/mathematik/mengenlehre/2_mengen.mdx
@@ -12,11 +12,11 @@ Diese Axiomatisierung wird hier allerdings nicht direkt vorgestellt oder explizi
 Stattdessen werden manche Axiome beiläufig eingeführt.
 Es können auch Axiome vorkommen, die in anderen Axiomatisierungen der Mengenlehre auftreten.
 
-## Mengenbildung
+## Mengenbildung {/* #mengenbildung */}
 *Bertrand Russell* entwickelte die *Typentheorie*, nach der man die Mengenlehre auch stufenweise aufbauen kann.
 Hierbei gibt es eine kleinste Stufe, deren Elemente man *Urelemente* oder *Urmengen* nennt.
 
-:::note Stufenaufbau nach Russell
+:::note[Stufenaufbau nach Russell]
 
 $$
     \begin{array}{c|c||c}
@@ -32,7 +32,7 @@ $$
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele */}
 Dabei sind die Elemente der jeweiligen Stufe stets Elemente der vorigen Stufe.
 
 Eine Menge von Urelementen ist also eine Menge erster Stufe: $M^1 = \{ X^0, Y^0 \} = \{ a, b \} = A$.
@@ -43,7 +43,7 @@ Mengensysteme spielen u.a. in der Maßtheorie eine wichtige Rolle, in der auch d
 
 Folgendes Axiom bildet eine Brücke zur Logik:
 
-:::tip Mengenbildungsaxiom
+:::tip[Mengenbildungsaxiom]
 
 Sei $H(M^n)$ Aussage über Mengen $n$-ter Stufe.
 $$
@@ -56,7 +56,7 @@ wobei $M^{n+1}$ nicht in $H(M^n)$ vorkommt.
 :::
 Das Mengenbildungsaxiom sagt aus, dass es eine Menge $M^{n+1}$ gibt, die aus den Elementen $M^n$ besteht, die eine gewisse Aussage erfüllen. 
 
-#### Beispiele
+#### Beispiele {/* #beispiele-1 */}
 Sei $n = 0$, dann können wir die Aussage im Satz mit den üblichen Benennungen wie folgt schreiben:
 $$
     \begin{equation*}
@@ -75,7 +75,7 @@ So eine Aussagenform $H(x)$ nennt man auch *definierenden Ausdruck*.
 Man schreibt Mengen mit definierenden Ausdrücken häufig so:
 $M = \{ x\ |\ H(x) \}$.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-2 */}
 Das obige Beispiel mit den geraden natürlichen Zahlen schreibt man also so:
 $M = \{ x\ |\ x \in \mathbb{N} \wedge x \text{ gerade} \}$
 
@@ -85,7 +85,7 @@ Weitere Beispiele sind:
 - Menge der ganzzahligen Lösungen einer Gleichung: $M = \{ x\ |\ x \in \mathbb{Z} \wedge x^2 + 2 = 4x - 1 \}$
 - Menge aller ganzen Quadratzahlen: $M = \{ x\ |\ \exists y \in \mathbb{Z} \colon x = y^2 \}$
 
-:::note Extensionalitätsaxiom (ZF) / Gleichheit von Mengen
+:::note[Extensionalitätsaxiom (ZF) / Gleichheit von Mengen]
 
 Zwei Mengen sind gleich, wenn sie die gleichen Elemente besitzen:
 $$
@@ -96,13 +96,13 @@ $$
 
 :::
 
-## Mengenalgebra
+## Mengenalgebra {/* #mengenalgebra */}
 Auf Mengen kann verschiedene Operationen durchführen.
 Man stelle sich vor, man möchte zwei Mengen zusammenfassen zu einer oder man möchte eine Menge erzeugen, 
 die nur die Elemente enthält, die zwei Mengen gemeinsam haben.
 Diese Mengenoperationen werden im folgenden vorgestellt.
 
-### Mengenoperationen
+### Mengenoperationen {/* #mengenoperationen */}
 Charakteristisch für Mengenoperationen ist, dass sie direkt auf den logischen Operatoren basieren und das auch in ihren
 Operationssymbolen wiederspiegeln.
 Zwischen den Mengen- und den Logikoperatoren besteht also eine enge Verbindung, 
@@ -115,11 +115,11 @@ Diese Ovale können überlappen, um zu zeigen, dass sie Elemente gemeinsam haben
 Der in lila eingefärbte Bereich ist dann die neue Menge, die entsteht, wenn man eine Mengenoperation auf den vorhanden Mengen ausführt.
 Eine solche Darstellung nennt man *Venn-Diagramm*[^2].
 
-#### Durchschnitt
+#### Durchschnitt {/* #durchschnitt */}
 Die Menge die entsteht, wenn man nur die Elemente aus zwei gegebenen Mengen nimmt, die sie gemeinsam haben nennt man *Durchschnitt*
 oder *Schnittmenge*.
 
-:::note Durchschnitt
+:::note[Durchschnitt]
 
 $$
     A \cap B \coloneqq \{ x\ |\ x \in A \wedge x \in B \}
@@ -132,7 +132,7 @@ Zugehöriges Venn-Diagramm:
 
 ![Venn Diagramm zum Mengen-Durchschnitt](/img/mathematik/mengenlehre/durchschnitt.png)
 
-##### Beispiele
+##### Beispiele {/* #beispiele-3 */}
 Gegeben seien $A = \{ a, b, c \}$ und $B = \{ b, c, d \}$.
 Dann ist $A \cap B = \{ b, c \}$.
 
@@ -147,12 +147,12 @@ Die beiden Mengen $A$ und $B$ sind gleich - entsprechend auch deren Durchschnitt
 Gegeben seien $A = \{ x\ |\ x \in \mathbb{N} \wedge x \text{ ist gerade} \}$ und $B = \{ 2, 8, 1001, 4088, 9999 \}$.
 Dann ist $A \cap B = \{2, 8, 4088 \}$.
 
-#### Vereinigung
+#### Vereinigung {/* #vereinigung */}
 Die Menge die entsteht, wenn man die Elemente aus zwei gegebenen Mengen nimmt, und sie in einer Menge *vereinigt*
 nennt man *Vereinigung* oder *Vereinigungsmenge*.
 Elemente, die in beiden vorkommen, werden dabei nur einmal gezählt.
 
-:::note Vereinigung
+:::note[Vereinigung]
 
 $$
     A \cup B \coloneqq \{ x\ |\ x \in A \vee x \in B \}
@@ -165,7 +165,7 @@ Zugehöriges Venn-Diagramm:
 
 ![Venn Diagramm zum Mengen-Durchschnitt](/img/mathematik/mengenlehre/vereinigung.png)
 
-##### Beispiele
+##### Beispiele {/* #beispiele-4 */}
 Gegeben seien $A = \{ a, b, c \}$ und $B = \{ b, c, d \}$.
 Dann ist $A \cup B = \{ a, b, c, d \}$.
 
@@ -176,10 +176,10 @@ Gegeben seien $A = \{ a, b, c \}$ und $B = \{ a, b, c \}$.
 Dann ist $A \cup B = \{ a, b, c \} = A = B$.
 Die beiden Mengen $A$ und $B$ sind gleich - entsprechend auch deren Vereinigung.
 
-#### Komplement
+#### Komplement {/* #komplement */}
 Das *Komplement* einer Menge besteht gerade aus den Elementen, die nicht in der Menge $A$ liegen, also alles andere außer die Menge $A$.
 
-:::note Komplement
+:::note[Komplement]
 
 $$
     \overline{A} = A^\complement \coloneqq \{ x\ |\ \neg (x \in A) \} = \{ x\ |\ x \notin A \}
@@ -192,7 +192,7 @@ Zugehöriges Venn-Diagramm:
 
 ![Venn Diagramm zum Mengen-Durchschnitt](/img/mathematik/mengenlehre/komplement.png)
 
-##### Beispiele
+##### Beispiele {/* #beispiele-5 */}
 Gegeben seien $M = \{ a, b, c, d, e \}$ und $A = \{ b, c, d \}$.
 Dann ist $\overline{A} = \{ a, e \}$.
 Hier ist es wichtig, dass wir $A$ in einen Bezug zu einer anderen "Übermenge" $M$ setzen.
@@ -202,11 +202,11 @@ Die Menge $A$ ist ein Teil des Universums $M$.
 Gegeben sei das Universum $A = \{ b, c, d \}$.
 Dann ist $\overline{A} = \emptyset$.
 
-#### Differenz
+#### Differenz {/* #differenz */}
 Wenn man zwei Mengen hat und man möchte eine Menge bilden, die nur die Elemente enthält, die in einer Menge vorkommen, 
 aber ohne die Elemente, die auch in der anderen liegen, dann ist das die *Differenzmenge* oder *Mengendifferenz*.
 
-:::note Differenz
+:::note[Differenz]
 
 $$
     A \setminus B \coloneqq \{ x\ |\ x \in A \wedge x \notin B \}
@@ -223,7 +223,7 @@ Zugehöriges Venn-Diagramm:
 Für die Differenz und das Komplement gilt eine besondere Beziehung:
 Sei $M$ das Universum und $A$ Teil des Universums, dann gilt: $M \setminus A = \overline{A}$.
 
-##### Beispiele
+##### Beispiele {/* #beispiele-6 */}
 Gegeben seien $A = \{ a, b, c, d \}$ und $B = \{ b, c, d, e \}$.
 Dann ist $A \setminus B = \{ a \}$.
 
@@ -236,10 +236,10 @@ Dann ist $M \setminus A = \{ a, d \} = \overline{A}$.
 Die Mengenoperationen wurden anhand Mengen 1. Stufe eingeführt, wie es die Symboliken erahnen lassen.
 Jedoch gelten diese auch für Mengen höherer Stufen.
 
-### Rechenregeln für Mengenoperationen
+### Rechenregeln für Mengenoperationen {/* #rechenregeln-für-mengenoperationen */}
 Für die Mengenoperationen gibt es gewisse Rechenregeln, die hier nun vorgestellt werden sollen.
 
-:::tip Rechenregeln für Mengenoperationen
+:::tip[Rechenregeln für Mengenoperationen]
 
 1. $$
    \begin{align*}
@@ -294,7 +294,7 @@ so ist es keineswegs sicher, dass es im Allgemeinen gilt.
 In der Mathematik muss man auch solche Kleinigkeiten beweisen.
 Also folgt an dieser Stelle ein erster Beweis für die Assoziativität des Durchschnitts:
 
-#### Beweis
+#### Beweis {/* #beweis */}
 Zu zeigen ist: $(A \cap B) \cap C = A \cap (B \cap C)$
 $$
 \begin{alignat*}{2}
@@ -313,13 +313,13 @@ Das $\blacksquare$ markiert schließlich das Ende des Beweises.
 
 Nach ähnlichem Schema können nun auch die anderen Regeln bewiesen werden.
 
-### Teilmenge
+### Teilmenge {/* #teilmenge */}
 In den Beispielen beim [Komplement](#beispiele-5) tauchte folgender Satz auf:
 > Die Menge $A$ ist ein Teil des Universums $M$.
 
 Dieses Wort "Teil" lässt sich wie folgt definieren:
 
-:::note Inklusion
+:::note[Inklusion]
 
 Seien $M, A$ Mengen.
 - $A \subseteq M \coloneqq \forall x \colon x \in A \rightarrow x \in M$
@@ -332,7 +332,7 @@ für $A \subset M$ spricht man "$A$ ist *echte Teilmenge* von $M$"
 Eine Teilmenge $A$ ist also mit ihren Elementen ganz und gar in ihrer *Obermenge* $M$ enthalten.
 Man bezeichnet diese Teilmengenbeziehung auch als *Inklusion*.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-7 */}
 Gegeben seien $M = \{ a, b, c, d \}$ und $A = \{ a, b \}$.
 Dann gilt $A \subseteq M$. 
 Es gilt sogar $A \subset M$.
@@ -343,13 +343,13 @@ Dann gilt $A \subseteq M$, aber nicht $A \subset M$.
 Gegeben seien $M = \{ a, b, c, d \}$ und $A = \{ e, f, g \}$.
 Dann gilt $A \not\subseteq M$.
 
-### Verband
+### Verband {/* #verband */}
 In der Mathematik untersucht man viele Strukturen.
 Strukturen sind dabei meist eine Menge mit zusätzlichen Dingen, wie Operationen.
 Die formale Definition einer ($n$-stelligen) Operation erfolgt später.
 Hier sei nur gesagt, dass $\cap$ und $\cup$ *zweistellige Operationen* sind.
 
-:::note Verband
+:::note[Verband]
 
 Seien $\mathfrak{M}$ Menge und $\cap, \cup$ zweistellige Operationen in $\mathfrak{M}$.
 
@@ -371,11 +371,11 @@ Wie diese Operation aussieht ist egal.
 Es kann also auch eine völlig andere Operation gewählt werden, solange sie die Rechenregeln erfüllt ist es ein Verband.
 $\cap$ und $\cup$ stehen also lediglich für ein Symbol, das gegen ein anderes Symbol und entsprechender Bedeutung ausgetauscht werden kann.
 
-### Potenzmenge
+### Potenzmenge {/* #potenzmenge */}
 Eine wichtige Menge (mindestens) zweiter Stufe ist die *Potenzmenge*.
 Die *Menge aller Teilmengen*.
 
-:::note Potenzmenge
+:::note[Potenzmenge]
 
 Sei $M$ Menge, dann heißt $2^M = \mathcal{P}(M) = \{ A\ |\ A \subseteq M \}$ *Potenzmenge* von $M$.
 
@@ -384,7 +384,7 @@ Die Bezeichnung $2^M$ kommt daher, da die Anzahl der Elemente in der Potenzmenge
 Wenn also $M$ drei Elemente enthält, dann hat $\mathcal{P}(M)$ $2^3 = 8$ Elemente.
 Die Anzahl der Elemente einer Menge wird im Abschnitt [Endlichkeit und Kardinalzahlen](./endlichkeit) weiter thematisiert.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-8 */}
 Gegeben sei $M = \{ a, b, c \}$.
 Dann ist $\mathcal{P}(M) = \{ \emptyset, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, M \}$ Potenzmenge von $M$.
 Man beachte, dass insbesondere auch die leere Menge $\emptyset$ und die Menge $M$ selbst Teilmengen von $M$ sind.
diff --git a/docs/mathematik/mengenlehre/mengenlehre.mdx b/docs/mathematik/mengenlehre/mengenlehre.mdx
index 49ab213..6200135 100644
--- a/docs/mathematik/mengenlehre/mengenlehre.mdx
+++ b/docs/mathematik/mengenlehre/mengenlehre.mdx
@@ -5,7 +5,7 @@ sidebar_position: 1
 ---
 
 # Mengenlehre
-## Themen
+## Themen {/* #themen */}
 In diesem Teil möchte ich über folgende Themen sprechen:
 
 1. [Elemente der Logik](logik)
@@ -18,7 +18,7 @@ In diesem Teil möchte ich über folgende Themen sprechen:
 4. [Verallgemeinerte mengentheoretische Relationen](verallgemeinerte_relationen)
 5. [Endlichkeit und Kardinalzahlen](endlichkeit)
 
-## Über die Mengenlehre
+## Über die Mengenlehre {/* #über-die-mengenlehre */}
 Die Logik und die Mengenlehre sind eng miteinander verknüpft und bilden die allgemeinen Grundlagen der Mathematik.
 Sie wurde von [Georg Cantor](https://de.wikipedia.org/wiki/Georg_Cantor) im 19. Jahrh. begründet.
 Cantor definierte dabei, was man unter einer *Menge* versteht und untersuchte diese Strukturen dann, u.a. die *Mächtigkeit* von Mengen.
@@ -35,8 +35,8 @@ Allerdings führte das Cantor'sche Modell der Mengenlehre, auch *naive Mengenleh
 Die heutige Mathematik beruht auf einer axiomatisierten Mengenlehre und wird auch *Zermelo-Fraenkel-Mengenlehre mit Auswahlaxiom* genannt.
 Doch ist die naive Mengenlehre ein Teil der ZFC-Mengenlehre (**Z**ermelo, **F**raenkel, Axiom of **C**hoice) und daher nach wie vor ein einfacher und guter Zugang.
 
-## Naive Mengenlehre nach Cantor
-:::note Menge
+## Naive Mengenlehre nach Cantor {/* #naive-mengenlehre-nach-cantor */}
+:::note[Menge]
 
 Unter einer *Menge* verstehen wir jede Zusammenfassung $M$ von bestimmten wohlunterschiedenen Objekten $m$ 
 unserer Anschauung oder unseres Denkens zu einem Ganzen.
@@ -47,26 +47,26 @@ Mengen werden dabei mit den *Mengenklammern* $\{$ und $\}$ aufgeschrieben.
 Außerdem wird das Symbol $\in$ dafür verwendet um zu beschreiben, dass ein *Element* $m$ zu einer Menge $M$ gehört: $m \in M$.
 Dagegen wird $\notin$ dafür verwendet, um zu beschreiben, dass ein Element $n$ nicht zur Menge $M$ gehört: $n \notin M$.
 
-### Beispiele für Mengen
-#### Ziffern 0 bis 5
+### Beispiele für Mengen {/* #beispiele-für-mengen */}
+#### Ziffern 0 bis 5 {/* #ziffern-0-bis-5 */}
 Die Menge der Ziffern *0* bis *5*:
 $$
 Z = \{ 0, 1, 2, 3, 4, 5 \}
 $$
 Dabei gilt z.B. $1 \in Z$ und $4 \in Z$, aber nicht $8 \in Z$, also $8 \notin Z$.
 
-#### Ballarten
+#### Ballarten {/* #ballarten */}
 Folgendes könnte eine Menge von verschiedenen, aber nicht allen Ballarten sein:
 $$
 B = \{ \text{Fußball}, \text{Tennisball}, \text{Baseball} \}
 $$
 Es gilt z.B. $\text{Fußball} \in B$ und $\text{Basketball} \notin B$.
 
-### Antinomien
+### Antinomien {/* #antinomien */}
 Diese *naive* Auffassung von Menge birgt allerdings Widersprüche, auch *Antinomien* genannt.
 
-#### Russell'sche Menge
-:::note Russell'schen Menge
+#### Russell'sche Menge {/* #russellsche-menge */}
+:::note[Russell'schen Menge]
 
 Menge aller Mengen, die sich nicht selbst als Element enthalten.
 
@@ -77,7 +77,7 @@ $$$
 A \in X \text{ genau dann, wenn } A \notin A
 $$$
 
-:::danger Aber gilt nun $X \in X$?
+:::danger[Aber gilt nun $X \in X$?]
 
 Für $A \coloneqq X$ erhält man den Widerspruch
 $$
@@ -90,10 +90,10 @@ Das funktioniert eben nicht: Wenn die Menge $X$ in $X$ selbst als Element liegt,
 da wir die Menge $X$ ja gerade so definiert haben, dass sie nur die Mengen enthält, die sich nicht selbst enthalten.
 Andersherum heißt es, dass wenn $X$ nicht in $X$ ist, dann müsste sie in $X$ liegen wegen der Definition von $X$.
 
-#### Barbier von Sevilla
+#### Barbier von Sevilla {/* #barbier-von-sevilla */}
 Ein anderes Beispiel ist die Anekdote vom *Barbier von Sevilla*, die ebenfalls von Russell stammt.
 
-:::note Barbier von Sevilla
+:::note[Barbier von Sevilla]
 
 Der Barbier $B$ ist derjenige Mann von Sevilla, der genau die Männer $M$ von Sevilla rasiert, die sich nicht selbst rasieren.
 
@@ -108,7 +108,7 @@ $$$
 M \in B \text{ genau dann, wenn } M \notin M
 $$$
 
-:::danger Rasiert der Barbier sich selbst?
+:::danger[Rasiert der Barbier sich selbst?]
 
 Für $M \coloneqq B$ erhält man den Widerspruch
 $$
diff --git a/docs/mathematik/mengenlehre/relationen/1_kartesisches_produkt_relationen.mdx b/docs/mathematik/mengenlehre/relationen/1_kartesisches_produkt_relationen.mdx
index e16a008..cb6520a 100644
--- a/docs/mathematik/mengenlehre/relationen/1_kartesisches_produkt_relationen.mdx
+++ b/docs/mathematik/mengenlehre/relationen/1_kartesisches_produkt_relationen.mdx
@@ -9,8 +9,8 @@ d.h. sie sind einfach in der Menge ohne Bedeutung und ohne Reihenfolge.
 Manchmal benötigt man jedoch so etwas wie eine Reihenfolge oder 
 möchte Mengen miteinander in eine gewisse Verbindung bringen, ohne sie einfach nur zu Vereinigen.
 
-## Kartesisches Produkt
-:::note Geordnete Paare
+## Kartesisches Produkt {/* #kartesisches-produkt */}
+:::note[Geordnete Paare]
 
 Ein *geordnetes Paar* (*2-Tupel*) mit den Elementen $a$ und $b$ ist wie folgt als Menge definiert:
 $$
@@ -26,7 +26,7 @@ Ein Verband haben wir als ein *Tripel* eingeführt.
 Ein Tripel ist ein 3-Tupel.
 Allgemein lassen sich rekursiv n-Tupel wie folgt definieren:
 
-:::note n-Tupel
+:::note[n-Tupel]
 
 - 1-Tupel: $(x_1) = \{ x_1 \}$
 - 2-Tupel: $(x_1, x_2) = \{ \{x_1, x_2\}, \{x_1\} \}$
@@ -54,7 +54,7 @@ Wir wollen es an dieser Stelle allerdings dabei belassen und nehmen es einfach h
 Man kann nun Tupel zu einer Menge zusammenfassen.
 Die Menge aller Tupel von Mengen nennt man *kartesisches Produkt*:
 
-:::note Kartesisches Produkt
+:::note[Kartesisches Produkt]
 
 Seien $A$ und $B$ Mengen, dann ist das *kartesische Produkt* der Mengen $A$ und $B$ definiert als
 $$
@@ -70,18 +70,18 @@ erhalten wir die *n-fache kartesische Potenz*.
 
 :::
 
-## Relationen
+## Relationen {/* #relationen */}
 Das kartesische Produkt erlaubt es uns jetzt Paare in einer Menge zusammenzufassen.
 Daraus können wir nun eine Teilmenge betrachten.
 
-:::note Relation
+:::note[Relation]
 
 Seien $A$, $B$ Mengen.
 Man nennt $R$ *Relation* oder *Korrespondenz* __aus__ $A$ __in__ $B$ $\coloneqq\ R \subseteq A \times B$
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele */}
 Nehmen wir eine Menge mit drei Elementen $A = \{a_1, a_2, a_3\}$ und bilden alle möglichen Paare.
 Diese Paare fassen wir nun in einer Menge zusammen: 
 $$
@@ -110,10 +110,10 @@ Dennoch sollte man darauf achten, ob man gerade mit einer echten Funktion oder n
 wenn man mit diesen Begriffen jongliert.
 Funktionen werden aber sehr bald schon eingeführt.
 
-### Definitions- und Wertebereich
+### Definitions- und Wertebereich {/* #definitions--und-wertebereich */}
 Es ist sinnvoll Mengen zu definieren, die nur die Elemente ersten oder die zweiten Elemente einer Relation erfasst:
 
-:::note Definitions- und Wertebereich
+:::note[Definitions- und Wertebereich]
 
 - *Definitionsbereich* von $R$: 
    $$
@@ -128,7 +128,7 @@ Es ist sinnvoll Mengen zu definieren, die nur die Elemente ersten oder die zweit
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-1 */}
 Gegeben sei $A = \{1, 2, 3, 4, 5\}$, $B = \{a, b, c, d\}$ und $R = \{(1,a), (1,d), (2,b), (3,b), (4,d)\} \subseteq A \times B$.
 Dann sind:
 - $D(R) = \{ 1, 2, 3, 5 \}$
@@ -156,7 +156,7 @@ Dann sind:
 
 Je nachdem, ob der Definitions- oder Wertebereich die gesamte Menge $A$ bzw. $B$ umfasst gibt es verschiedene Sprechweisen.
 
-:::note Sprechweisen
+:::note[Sprechweisen]
 
 $R$ ist Relation
 - "*__von__* $A$ *in* $B$" $\coloneqq\ D(R) = A$
@@ -168,7 +168,7 @@ $R$ ist Relation
 Wenn nun eine Relation gegeben ist, dann möchte man vielleicht die Frage stellen "Welche $y$-Werte werden für ein $x$ angenommen?"
 und möchte dies formal ausdrücken bzw. aufschreiben, ohne dabei immer die Tupel angeben zu müssen.
 
-:::note Schreibweise 1
+:::note[Schreibweise 1]
 
 Sei $R$ Relation.
 $$
@@ -177,7 +177,7 @@ $$
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-2 */}
 Gegeben sei $A = \{1, 2, 3, 4, 5\}$, $B = \{a, b, c, d\}$ und $R = \{(1,a), (1,d), (2,b), (3,b), (4,d)\} \subseteq A \times B$.
 Dann ist:
 $$
@@ -197,7 +197,7 @@ Man erkennt an diesem Beispiel schon einen gewissen Aufbau: "$x$ ist verwandt mi
 Häufig schreibt man in so einem Fall also nicht $(x,y) \in R$ oder $R(x) = \{y, (\dots)\}$, sondern zieht die
 Relationsbezeichnung in die Mitte:
 
-:::note Schreibweise 2
+:::note[Schreibweise 2 (Infix-Schreibweise)]
 
 Sei $R$ Relation.
 $$
@@ -206,7 +206,7 @@ $$
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-3 */}
 Sei $R$ jeweils die Relation in den Stichpunkten.
 Statt $x R y$ schreibt man in konkreten Fällen dann:
 - $x$ ist verwandt mit $y$
@@ -219,10 +219,10 @@ Wir werden uns später noch mit Ordnungsrelationen und Operationen beschäftigen
 Aber an dieser Stelle sind es nur symbolische Beispiele, wieso es sinnvoll ist, manche Relationen in dieser Schreibweise zu präsentieren.
 
 
-### Verkettung und Inverse
+### Verkettung und Inverse {/* #verkettung-und-inverse */}
 Man kann auch zwei Relationen kombinieren, sofern diese *in* und *aus* den gleichen Mengen korrespondieren - in dieser Reihenfolge.
 
-:::note Verkettung / Relationenprodukt
+:::note[Verkettung / Relationenprodukt]
 
 Seien $R \subseteq A \times B$ und $K \subseteq B \times C$ Relationen.
 Dann ist die Verkettung von $R$ mit $K$ definiert als:
@@ -233,7 +233,7 @@ Also ist $R \circ K \subseteq A \times C$.
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-4 */}
 Gegeben seien $A = \{1, 2, 3, 4, 5\}$, $B = \{a, b, c, d\}$ und $C = \{\alpha, \beta, \gamma\}$.
 $R = \{(1,a), (1,d), (2,b), (3,b), (4,d)\} \subseteq A \times B$ und 
 $K = \{(a, \alpha), (a, \beta), (a, \gamma), (b, \beta), (c, \alpha)\} \subseteq B \times C$ seien Relationen.
@@ -256,7 +256,7 @@ Relationen kann man auch umkehren.
 Die Rolle der ersten Elemente eines Tupels vertauscht sich dann mit den zweiten Elementen.
 Das heißt, wenn $x$ mit $y$ in Relation steht, also $(x,y) \in R$, dann ist das *Inverse* dazu $(y,x) \in R^{-1}$.
 
-:::note Inverse Relation
+:::note[Inverse Relation]
 
 Gegeben sei $R \subseteq A \times B$
 $$
@@ -268,7 +268,7 @@ ist die *inverse Relation* zu $R$.
 Man beachte, dass sich entsprechend das kartesische Produkt umdreht.
 Also wenn $R \subseteq A \times B$, dann ist $R^{-1} \subseteq B \times A$.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-5 */}
 Gegeben seien $A = \{1, 2, 3, 4, 5\}$, $B = \{a, b, c, d\}$ und $R = \{(1,a), (1,d), (2,b), (3,b), (4,d)\} \subseteq A \times B$.
 Das Inverse $R^{-1}$ von $R$ ist jetzt jedes Paar aus $R$ umgedreht:
 $$
@@ -279,7 +279,7 @@ Veranschaulicht:
 ![Relation R und Inverse von R veranschaulicht durch Pfeile](/img/mathematik/mengenlehre/relationen/inverse_rel.png)
 
 Für die Verkettung und das Inverse gelten nun folgende Eigenschaften:
-:::tip Sätze über Verkettung und Inverse von Relationen
+:::tip[Sätze über Verkettung und Inverse von Relationen]
 
 1. Die Verkettung ist assoziativ: $(R \circ K) \circ F = R \circ (K \circ F )$
 2. $(R^{-1})^{-1} = R$
@@ -295,7 +295,7 @@ Trivial ist eine oft benutzte Bezeichnung in der Mathematik, wenn etwas offensic
 also so leicht, dass man keinen extra beweis dafür angibt - dennoch gibt es Fallen und es sollte nicht leichtfertig benutzt werden.
 In diesem Fall mache man sich klar, dass 2. wirklich gilt und beweise es sogar.
 
-#### Beweis von 3
+#### Beweis von 3 {/* #beweis-von-3 */}
 Der dritte Satz ist eine schöne Beziehung zwischen Verkettung und den inversen Relationen.
 $$
 \begin{alignat*}{2}
diff --git a/docs/mathematik/mengenlehre/relationen/2_abbildungen.mdx b/docs/mathematik/mengenlehre/relationen/2_abbildungen.mdx
index 87959db..1a934cc 100644
--- a/docs/mathematik/mengenlehre/relationen/2_abbildungen.mdx
+++ b/docs/mathematik/mengenlehre/relationen/2_abbildungen.mdx
@@ -8,10 +8,10 @@ Eine der wichtigsten Relationen überhaupt stellen die *Abbildungen* da.
 Sie tauchen überall in der Mathematik auf und in der Realität lassen sich viele Probleme durch diese 
 speziellen Relationen darstellen.
 
-## Funktionen
+## Funktionen {/* #funktionen */}
 Bevor wir uns den Abbildungen widmen, definieren wir die Eindeutigkeit:
 
-:::note Eindeutigkeit
+:::note[Eindeutigkeit]
 
 Eine Relation $R \subseteq A \times B$ ist *eindeutig*, wenn
 $$
@@ -30,7 +30,7 @@ Bei der Eindeutigkeit ist es egal, wie viele Pfeile rechts auf ein Element zugeh
 
 ![Eindeutigkeit bei einer Relation dargestellt](/img/mathematik/mengenlehre/relationen/eindeutige_rel.png)
 
-:::note Abbildung / Funktion
+:::note[Abbildung / Funktion]
 
 $f$ ist *Abbildung* oder *Funktion* von $A$ in $B$ $:\Leftrightarrow$
 - $f$ ist Relation, also $f \subseteq A \times B$
@@ -50,7 +50,7 @@ Eine Funktion ordnet also jedem Element aus $A$ genau ein $y$ aus $B$ zu.
 
 In der Analysis und auch in anderen mathematischen Gebieten findet man häufig eine alternative textliche Einführung:
 
-:::note Alternative Definition
+:::note[Alternative Definition]
 
 Eine Abbildung oder eine Funktion einer Menge $A$ in eine Menge $B$ ordnet jedem Element $x \in A$ genau ein Element $y \in B$ zu.
 
@@ -59,7 +59,7 @@ Bei dieser Definition wird komplett auf die mengentheoretische Begriffe wie *geo
 Erst aufbauend darauf wird dann mengentheoretisch der *Graph der Funktion* definiert als $G_f \coloneqq \{(x,f(x))\ |\ x \in A \wedge f(x) \in B\} \subseteq A \times B$.
 Aus mengentheoretischer Sicht stimmen in diesen Fällen die Begriffe "Funktion" und "Graph der Funktion" überein.
 
-#### Beispiele
+#### Beispiele {/* #beispiele */}
 Gegeben seien $A = \{1, 2, 3, 4, 5\}$ und $B = \{a, b, c, d\}$.
 Eine Abbildung $f \colon A \rightarrow B$ können dann sein:
 - $f = \{(1,b)\}$
@@ -70,7 +70,7 @@ Eine Abbildung $f \colon A \rightarrow B$ können dann sein:
 Wenn man eine rechnerische Vorschrift (*Abbildungsvorschrift*) angeben möchte, wie ein $y$ zu einem $x$ berechnet werden soll, 
 dann schreibt man Abbildungen so:
 
-:::note Schreibweisen
+:::note[Schreibweisen]
 
 $$
     f \colon A \rightarrow B,\ x \mapsto f(x)
@@ -84,7 +84,7 @@ wobei anstelle $f(x)$ dann z.B. eine *Funktionsgleichung* tritt.
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-1 */}
 - $f \colon \mathbb{R} \rightarrow \mathbb{R},\ x \mapsto x^2 \quad$ für eine Parabel
 - $f \colon \begin{cases}
      \mathbb{N} \rightarrow \mathbb{R}\\
@@ -94,7 +94,7 @@ wobei anstelle $f(x)$ dann z.B. eine *Funktionsgleichung* tritt.
 Es werden noch mehr unterschiedliche Darstellungsformen für Funktionen auftauchen, je nachdem wie es gerade angebracht ist.
 Bis dahin sollten einem die Begriffe allerdings so vertraut vorkommen, dass eine genaue Definition oder Einführung nicht notwendig ist.
 
-## Grundlegende Eigenschaften von Funktionen
+## Grundlegende Eigenschaften von Funktionen {/* #grundlegende-eigenschaften-von-funktionen */}
 Die *Verkettung*, oder auch *Komposition*, $f \circ g \colon A \rightarrow C$ von Funktionen $f \colon A \rightarrow B$ und $g \colon B \rightarrow C$ ist wieder eine Funktion.
 Für die Komposition gilt $f \circ g = g(f(x))$.
 In anderer Literatur kann es sein, dass die Komposition anders definiert ist und dann $f \circ g = f(g(x))$ gilt.
@@ -103,7 +103,7 @@ Jedoch ist das *Inverse* $f^{-1}$ einer Funktion $f$ im Allgemeinen keine Funkti
 
 Zwei Funktionen $f$ und $g$ sind gleich $f=g$, wenn für alle $x$ gilt $f(x) = g(x)$.
 
-:::note Injektivität, Surjektivität, Bijektivität
+:::note[Injektivität, Surjektivität, Bijektivität]
 
 Sei $f: A \rightarrow B$ eine Funktion.
 - $f$ heißt *injektiv* (*eineindeutig*) $\coloneqq\ \forall x,x' \in A \colon f(x) = f(x') \rightarrow x = x'$
@@ -132,7 +132,7 @@ Es darf also kein Element aus $B$ frei bleiben und es darf nur genau ein Pfeil p
 Dass dabei $A$ und $B$ gleich viele Elemente haben müssen ist kein Zufall.
 Welche Rolle bijektive Abbildungen bei der *Kardinalität* ("Größe") von Mengen haben, wird im Kapitel [Endlichkeit und Kardinalzahlen](../endlichkeit) erklärt.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-2 */}
 Gegeben sei $f \colon \mathbb{N} \rightarrow \mathbb{N},\ n \mapsto f(n)$.
 Betrachten verschiedene Funktionsgleichungen für $f(n)$:
 - $f(n) \coloneqq n+1 \quad$ (*Nachfolgerfunktion*) ist injektiv, aber nicht surjektiv, da $0 \notin W(f)$
@@ -155,7 +155,7 @@ Eingangs wurde erwähnt:
 
 Im Falle einer bijektiven Abbildung $f$ ist $f^{-1}$ allerdings eine Abbildung und man nennt diese dann *Umkehrabbildung* oder *Umkehrfunktion*.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-3 */}
 Bei einer bijektiven Abbildung, die durch eine Funktionsgleichung $y = f(x)$ gegeben ist, kann man die Umkehrabbildung einfach dadurch berechnen,
 dass man die Funktionsgleichung nach $x$ umstellt.
 Man hat dann einen Ausdruck der Form $x = g(y) = f^{-1}(y)$.
@@ -176,7 +176,7 @@ $$
 \end{alignat*}
 $$
 
-## Erweiterung von Abbildungen
+## Erweiterung von Abbildungen {/* #erweiterung-von-abbildungen */}
 Gegeben seien $S$ als die Menge aller Schulkinder und $K$ als die Menge aller Klassen einer Schule.
 Als Abbildung definieren $k: S \rightarrow K$, die jedem Schulkind die eigene Klasse zuordnet.
 Der Direktor hat nun eine Liste von Schulkindern, mit denen er zusammen sprechen möchte.
@@ -192,7 +192,7 @@ Der Direktor hat eine Liste von Klassen und möchte nun wissen, welche Schulkind
 
 Formal lässt sich das so auffassen:
 
-:::note Erweiterung
+:::note[Erweiterung]
 
 Gegeben seien eine Abbildung $f \colon A \rightarrow B$ und die Teilmengen $X \subseteq A$ und $Y \subseteq B$.
 
@@ -212,7 +212,7 @@ Häufig schreibt man statt $\widehat{f}$ auch wieder nur $f$ bzw. für $\widehat
 Eine Verwechslung ist ausgeschlossen, da die Abbildung $f$ ein Element entgegennimmt, 
 während die Erweiterung von $f$ eine Menge entgegennimmt.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-4 */}
 Gegeben sei $f \colon \{1, 2, 3\} \rightarrow \{a, b, c, d\}$ mit $f(1) = a,\ f(2) = c,\ f(3) = a$.
 Dann sind bspw.:
 - $\widehat{f}(\emptyset) = f(\emptyset) = \emptyset$
@@ -227,12 +227,12 @@ und
 - $\widehat{f^{-1}}(\{b, d\}) = f^{-1}(\{b, d\}) = \emptyset$
 - $f^{-1}(\{a, b, c, d\}) = f^{-1}(D(f^{-1})) = \{ 1, 2, 3 \} = W(f^{-1})$
 
-## Operationen
+## Operationen {/* #operationen */}
 Im Kapitel [Kartesisches Produkt](kartesisches_produkt_relationen#kartesisches-produkt) wurde bereits die *kartesische Potenz* eingeführt.
 Mit den kartesischen Potenzen führen wir nun eine weitere wichtige Klasse von Abbildungen ein, die *Operationen* oder *Verknüpfungen*.
 Diese spielen in der Algebra eine wichtige Rolle.
 
-:::note Operation oder Verknüpfung
+:::note[Operation oder Verknüpfung]
 
 $f$ heißt *innere $n$-stellige algebraische Operation* $\coloneqq\ f \colon A^n \rightarrow A$.
 
@@ -247,7 +247,7 @@ $2$-stellige Relationen heißen auch *binäre Relationen*.
 Entsprechend heißen $2$-stellige Operationen auch binäre Operation.
 Bereits im Kapitel [Verband](../mengen#verband) wurden zweistellige Operationen das erste Mal genannt.
 
-#### Beispiele
+#### Beispiele {/* #beispiele-5 */}
 Aus dem Kapitel [Verband](../mengen#verband) wissen wir, dass $\cap$ und $\cup$ zweistellige Operationen für eine Menge $A$ sind:
 - $\cap \colon \mathcal{P}^2(A) \rightarrow \mathcal{P}(A)$
 - $\cup \colon \mathcal{P}^2(A) \rightarrow \mathcal{P}(A)$
diff --git a/docs/mathematik/mengenlehre/relationen/3_aequivalenzrelationen.mdx b/docs/mathematik/mengenlehre/relationen/3_aequivalenzrelationen.mdx
index aa00d16..99c0e7c 100644
--- a/docs/mathematik/mengenlehre/relationen/3_aequivalenzrelationen.mdx
+++ b/docs/mathematik/mengenlehre/relationen/3_aequivalenzrelationen.mdx
@@ -10,7 +10,7 @@ Die Äquivalenzrelationen und die mit diesen eng zusammenhängenden *Äquivalenz
 # Äquivalenzrelationen
 Bevor wir die Äquivalenzrelationen formal einführen, widmen wir uns erst nochmal ein paar wichtige Einordnungen Relationen betreffend.
 
-:::note Reflexivität / Symmetrie / Transitivität
+:::note[Reflexivität, Symmetrie und Transitivität]
 
 Sei $M$ eine Menge und $\varrho \subseteq M \times M$ eine Relation.
 - $\varrho$ heißt *reflexiv* $:\Leftrightarrow \forall x \in M \colon (x,x) \in \varrho$
@@ -19,7 +19,7 @@ Sei $M$ eine Menge und $\varrho \subseteq M \times M$ eine Relation.
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele */}
 Gegeben sei die Menge $M = \{a,b,c\}$.
 - $\varrho = \{(a,a), (b,b), (c,c), (a,b), (a,c)\}$ ist reflexiv,
     da die Paare $(a,a)$, $(b,b)$ und $(c,c)$ in $\varrho$ sind.\
@@ -35,13 +35,13 @@ Gegeben sei die Menge $M = \{a,b,c\}$.
 
 Eine Relation, die nun all diese drei Eigenschaften zugleich erfüllt nennt sich *Äquivalenzrelation*.
 
-:::note Äquivalenzrelation
+:::note[Äquivalenzrelation]
 
 Sei $M$ eine Menge und $\varrho \subseteq M \times M$ eine Relation.
 $\varrho$ heißt *Äquivalenzrelation*, falls $\varrho$ reflexiv, symmetrisch und transitiv ist.
 
 :::
 
-#### Beispiele
+#### Beispiele {/* #beispiele-1 */}
 Die wohl bekannteste Äquivalenzrelation auf jeder Menge $M$ ist die Gleichheit $=$ mit ihren üblichen Eigenschaften.
 Äquivalenz in der Logik ist ebenfalls eine Äquivalenzrelation.
\ No newline at end of file
diff --git a/docusaurus.config.js b/docusaurus.config.js
index 8fd64e8..57cfde1 100644
--- a/docusaurus.config.js
+++ b/docusaurus.config.js
@@ -5,7 +5,7 @@ import remarkMath from 'remark-math';
 import rehypeKatex from 'rehype-katex';
 
 const lightCodeTheme = require('prism-react-renderer').themes.github;
-const darkCodeTheme = require('prism-react-renderer').themes.dracula;
+const darkCodeTheme = require('prism-react-renderer').themes.catppuccin;
 
 /** @type {import('@docusaurus/types').Config} */
 export default {
@@ -14,9 +14,14 @@ export default {
     url: 'https://www.niklas-birk.de',
     baseUrl: '/',
     onBrokenLinks: 'warn',
-    onBrokenMarkdownLinks: 'warn',
     favicon: 'img/niklas-birk-icon.ico',
 
+    markdown: {
+        hooks: {
+            onBrokenMarkdownLinks: 'warn',
+        }
+    },
+
     // GitHub pages deployment config.
     // If you aren't using GitHub pages, you don't need these.
     // organizationName: 'niklas', // Usually your GitHub org/user name.
@@ -116,10 +121,10 @@ export default {
                     {
                         title: 'Socials',
                         items: [
-                            {
-                                label: 'Twitter',
-                                href: 'https://twitter.com/theoremofnik',
-                            },
+                            // {
+                            //     label: 'Twitter',
+                            //     href: 'https://twitter.com/theoremofnik',
+                            // },
                             {
                                 label: 'Mastodon',
                                 href: 'https://mathstodon.xyz/web/@SirNik',
@@ -156,7 +161,7 @@ export default {
                 copyright: `Copyright © ${new Date().getFullYear()} Niklas Birk. Built with Docusaurus.`,
             },
             prism: {
-                theme: lightCodeTheme,
+                theme: darkCodeTheme,
                 darkTheme: darkCodeTheme,
             },
         }),
@@ -171,6 +176,7 @@ export default {
         },
     ],
     future: {
-        experimental_faster: true,
+            v4: true,
+        faster: true,
     }
 };
\ No newline at end of file
diff --git a/package-lock.json b/package-lock.json
index a131a93..44f63af 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,72 +1,89 @@
 {
   "name": "niklas-birk-blog",
-  "version": "0.1.1",
+  "version": "0.1.2",
   "lockfileVersion": 3,
   "requires": true,
   "packages": {
     "": {
       "name": "niklas-birk-blog",
-      "version": "0.1.1",
+      "version": "0.1.2",
       "dependencies": {
-        "@docusaurus/core": "^3.7.0",
-        "@docusaurus/faster": "^3.7.0",
-        "@docusaurus/preset-classic": "^3.7.0",
-        "@mdx-js/react": "^3.1.0",
+        "@docusaurus/core": "^3.10.2",
+        "@docusaurus/faster": "^3.10.2",
+        "@docusaurus/preset-classic": "^3.10.2",
+        "@mdx-js/react": "^3.1.1",
         "clsx": "^2.1.1",
         "hast-util-is-element": "^3.0.0",
         "prism-react-renderer": "^2.4.1",
-        "react": "^19.0.0",
-        "react-dom": "^19.0.0",
+        "react": "^19.3.0",
+        "react-dom": "^19.3.0",
         "rehype-katex": "^7.0.1",
         "remark-math": "^6.0.0"
       },
       "devDependencies": {
-        "@docusaurus/module-type-aliases": "^3.7.0",
-        "@docusaurus/types": "3.7.0"
+        "@docusaurus/module-type-aliases": "^3.10.2",
+        "@docusaurus/types": "^3.10.2"
       },
       "engines": {
         "node": ">=18.0"
       }
     },
-    "node_modules/@algolia/autocomplete-core": {
-      "version": "1.17.7",
-      "resolved": "https://registry.npmjs.org/@algolia/autocomplete-core/-/autocomplete-core-1.17.7.tgz",
-      "integrity": "sha512-BjiPOW6ks90UKl7TwMv7oNQMnzU+t/wk9mgIDi6b1tXpUek7MW0lbNOUHpvam9pe3lVCf4xPFT+lK7s+e+fs7Q==",
+    "node_modules/@11ty/gray-matter": {
+      "version": "1.0.0",
+      "resolved": "https://registry.npmjs.org/@11ty/gray-matter/-/gray-matter-1.0.0.tgz",
+      "integrity": "sha512-7mJJl+wf1AByoT0PknQiQfOPnVNT4fevGrUBVWO4HXsnYn1aQPyRyrELYrNUFleUBM++KzMKN6QaxHPk0t/6/g==",
       "license": "MIT",
       "dependencies": {
-        "@algolia/autocomplete-plugin-algolia-insights": "1.17.7",
-        "@algolia/autocomplete-shared": "1.17.7"
+        "js-yaml": "^4.1.0",
+        "kind-of": "^6.0.3",
+        "section-matter": "^1.0.0",
+        "strip-bom-string": "^1.0.0"
+      },
+      "engines": {
+        "node": ">=11"
+      }
+    },
+    "node_modules/@algolia/abtesting": {
+      "version": "1.25.0",
+      "resolved": "https://registry.npmjs.org/@algolia/abtesting/-/abtesting-1.25.0.tgz",
+      "integrity": "sha512-rSTin9Uta23uaewYVQEp8XI9T3iA/zrg0/1G2vhf8oFFDxFL5vybnZ5IQwsVAg4JpKxPX4/WYNKdcfWrZymk7w==",
+      "license": "MIT",
+      "dependencies": {
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
+      },
+      "engines": {
+        "node": ">= 14.0.0"
+      }
+    },
+    "node_modules/@algolia/autocomplete-core": {
+      "version": "1.19.11",
+      "resolved": "https://registry.npmjs.org/@algolia/autocomplete-core/-/autocomplete-core-1.19.11.tgz",
+      "integrity": "sha512-Txje8Sw5yMH4ApvgqR9rAxxWgmVKG+lIgl/e6MEn/IVkQvB/NZu7rV2+2Iy4/p34/D+DWS+hxpZL39w33pJXKA==",
+      "license": "MIT",
+      "dependencies": {
+        "@algolia/autocomplete-plugin-algolia-insights": "1.19.11",
+        "@algolia/autocomplete-shared": "1.19.11"
       }
     },
     "node_modules/@algolia/autocomplete-plugin-algolia-insights": {
-      "version": "1.17.7",
-      "resolved": "https://registry.npmjs.org/@algolia/autocomplete-plugin-algolia-insights/-/autocomplete-plugin-algolia-insights-1.17.7.tgz",
-      "integrity": "sha512-Jca5Ude6yUOuyzjnz57og7Et3aXjbwCSDf/8onLHSQgw1qW3ALl9mrMWaXb5FmPVkV3EtkD2F/+NkT6VHyPu9A==",
+      "version": "1.19.11",
+      "resolved": "https://registry.npmjs.org/@algolia/autocomplete-plugin-algolia-insights/-/autocomplete-plugin-algolia-insights-1.19.11.tgz",
+      "integrity": "sha512-NW7gVJqk1dQQeOEsY9+GqImCJwjL0YZW50gLDdfjI/9zfYNiCCByzpQaUM9YRzVr1QM61FHiVRjT6advLwl9Qw==",
       "license": "MIT",
       "dependencies": {
-        "@algolia/autocomplete-shared": "1.17.7"
+        "@algolia/autocomplete-shared": "1.19.11"
       },
       "peerDependencies": {
         "search-insights": ">= 1 < 3"
       }
     },
-    "node_modules/@algolia/autocomplete-preset-algolia": {
-      "version": "1.17.7",
-      "resolved": "https://registry.npmjs.org/@algolia/autocomplete-preset-algolia/-/autocomplete-preset-algolia-1.17.7.tgz",
-      "integrity": "sha512-ggOQ950+nwbWROq2MOCIL71RE0DdQZsceqrg32UqnhDz8FlO9rL8ONHNsI2R1MH0tkgVIDKI/D0sMiUchsFdWA==",
-      "license": "MIT",
-      "dependencies": {
-        "@algolia/autocomplete-shared": "1.17.7"
-      },
-      "peerDependencies": {
-        "@algolia/client-search": ">= 4.9.1 < 6",
-        "algoliasearch": ">= 4.9.1 < 6"
-      }
-    },
     "node_modules/@algolia/autocomplete-shared": {
-      "version": "1.17.7",
-      "resolved": "https://registry.npmjs.org/@algolia/autocomplete-shared/-/autocomplete-shared-1.17.7.tgz",
-      "integrity": "sha512-o/1Vurr42U/qskRSuhBH+VKxMvkkUVTLU6WZQr+L5lGZZLYWyhdzWjW0iGXY7EkwRTjBqvN2EsR81yCTGV/kmg==",
+      "version": "1.19.11",
+      "resolved": "https://registry.npmjs.org/@algolia/autocomplete-shared/-/autocomplete-shared-1.19.11.tgz",
+      "integrity": "sha512-9oYPEMmMAH+/EDUGKJJ6oX6JI7YNq7tmWTxEbe8r/qmZnM5BoJSzo8C3Wa2Kc/EPyBJjFrjw7qwo7huzqAYW0g==",
       "license": "MIT",
       "peerDependencies": {
         "@algolia/client-search": ">= 4.9.1 < 6",
@@ -74,99 +91,99 @@
       }
     },
     "node_modules/@algolia/client-abtesting": {
-      "version": "5.19.0",
-      "resolved": "https://registry.npmjs.org/@algolia/client-abtesting/-/client-abtesting-5.19.0.tgz",
-      "integrity": "sha512-dMHwy2+nBL0SnIsC1iHvkBao64h4z+roGelOz11cxrDBrAdASxLxmfVMop8gmodQ2yZSacX0Rzevtxa+9SqxCw==",
+      "version": "5.59.0",
+      "resolved": "https://registry.npmjs.org/@algolia/client-abtesting/-/client-abtesting-5.59.0.tgz",
+      "integrity": "sha512-bm2XN0hCSMYwStSsCBT0/PUB2BDxoyR1Lnub3c392HMEy9bi8PUSW8vR6zltVEKWG2t4PQFWMD5C07bmJxGgPg==",
       "license": "MIT",
       "dependencies": {
-        "@algolia/client-common": "5.19.0",
-        "@algolia/requester-browser-xhr": "5.19.0",
-        "@algolia/requester-fetch": "5.19.0",
-        "@algolia/requester-node-http": "5.19.0"
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
       },
       "engines": {
         "node": ">= 14.0.0"
       }
     },
     "node_modules/@algolia/client-analytics": {
-      "version": "5.19.0",
-      "resolved": "https://registry.npmjs.org/@algolia/client-analytics/-/client-analytics-5.19.0.tgz",
-      "integrity": "sha512-CDW4RwnCHzU10upPJqS6N6YwDpDHno7w6/qXT9KPbPbt8szIIzCHrva4O9KIfx1OhdsHzfGSI5hMAiOOYl4DEQ==",
+      "version": "5.59.0",
+      "resolved": "https://registry.npmjs.org/@algolia/client-analytics/-/client-analytics-5.59.0.tgz",
+      "integrity": "sha512-XOFPOTa69WuqHR6c5tMgnUUwwqQgNSzMpxmhrgA9KmxRf8WIqEa0cokHJvohk5CYb7CZx0xeSL6Bk2IUJ7Lv7Q==",
       "license": "MIT",
       "dependencies": {
-        "@algolia/client-common": "5.19.0",
-        "@algolia/requester-browser-xhr": "5.19.0",
-        "@algolia/requester-fetch": "5.19.0",
-        "@algolia/requester-node-http": "5.19.0"
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
       },
       "engines": {
         "node": ">= 14.0.0"
       }
     },
     "node_modules/@algolia/client-common": {
-      "version": "5.19.0",
-      "resolved": "https://registry.npmjs.org/@algolia/client-common/-/client-common-5.19.0.tgz",
-      "integrity": "sha512-2ERRbICHXvtj5kfFpY5r8qu9pJII/NAHsdgUXnUitQFwPdPL7wXiupcvZJC7DSntOnE8AE0lM7oDsPhrJfj5nQ==",
+      "version": "5.59.0",
+      "resolved": "https://registry.npmjs.org/@algolia/client-common/-/client-common-5.59.0.tgz",
+      "integrity": "sha512-PC8ipLOYFKRTfIUY1J3FJxS6ryzWziaXmIX9/sNMoUR8L+XhF7hX2QAeUI87YVl5zujvlYTSOb+HAIqKXDjyHQ==",
       "license": "MIT",
       "engines": {
         "node": ">= 14.0.0"
       }
     },
     "node_modules/@algolia/client-insights": {
-      "version": "5.19.0",
-      "resolved": "https://registry.npmjs.org/@algolia/client-insights/-/client-insights-5.19.0.tgz",
-      "integrity": "sha512-xPOiGjo6I9mfjdJO7Y+p035aWePcbsItizIp+qVyfkfZiGgD+TbNxM12g7QhFAHIkx/mlYaocxPY/TmwPzTe+A==",
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+      "resolved": "https://registry.npmjs.org/@algolia/client-insights/-/client-insights-5.59.0.tgz",
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       "dependencies": {
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-        "@algolia/requester-browser-xhr": "5.19.0",
-        "@algolia/requester-fetch": "5.19.0",
-        "@algolia/requester-node-http": "5.19.0"
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
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       "engines": {
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     },
     "node_modules/@algolia/client-personalization": {
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-      "resolved": "https://registry.npmjs.org/@algolia/client-personalization/-/client-personalization-5.19.0.tgz",
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-        "@algolia/requester-fetch": "5.19.0",
-        "@algolia/requester-node-http": "5.19.0"
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
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     "node_modules/@algolia/client-query-suggestions": {
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+      "version": "5.59.0",
+      "resolved": "https://registry.npmjs.org/@algolia/client-query-suggestions/-/client-query-suggestions-5.59.0.tgz",
+      "integrity": "sha512-Wofg7bMpWh8N5qDDZs0wy6whc+KMmdNsxgrIGp9Ug2s1Bka0uq7AjyckdxReKPHLA0Q1qH8X/SNh0wn2t2X2Lw==",
       "license": "MIT",
       "dependencies": {
-        "@algolia/client-common": "5.19.0",
-        "@algolia/requester-browser-xhr": "5.19.0",
-        "@algolia/requester-fetch": "5.19.0",
-        "@algolia/requester-node-http": "5.19.0"
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
       },
       "engines": {
         "node": ">= 14.0.0"
       }
     },
     "node_modules/@algolia/client-search": {
-      "version": "5.19.0",
-      "resolved": "https://registry.npmjs.org/@algolia/client-search/-/client-search-5.19.0.tgz",
-      "integrity": "sha512-Ctg3xXD/1VtcwmkulR5+cKGOMj4r0wC49Y/KZdGQcqpydKn+e86F6l3tb3utLJQVq4lpEJud6kdRykFgcNsp8Q==",
+      "version": "5.59.0",
+      "resolved": "https://registry.npmjs.org/@algolia/client-search/-/client-search-5.59.0.tgz",
+      "integrity": "sha512-fHnALZfbEnODczGk14Y/1YBRApp6UEpZUTexGcMUPzY7RDc7q4HN2Y6jh0KUG8Jo9B+q+wOoQEc3ziR0ErbuFg==",
       "license": "MIT",
       "dependencies": {
-        "@algolia/client-common": "5.19.0",
-        "@algolia/requester-browser-xhr": "5.19.0",
-        "@algolia/requester-fetch": "5.19.0",
-        "@algolia/requester-node-http": "5.19.0"
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
       },
       "engines": {
         "node": ">= 14.0.0"
@@ -179,138 +196,125 @@
       "license": "MIT"
     },
     "node_modules/@algolia/ingestion": {
-      "version": "1.19.0",
-      "resolved": "https://registry.npmjs.org/@algolia/ingestion/-/ingestion-1.19.0.tgz",
-      "integrity": "sha512-LO7w1MDV+ZLESwfPmXkp+KLeYeFrYEgtbCZG6buWjddhYraPQ9MuQWLhLLiaMlKxZ/sZvFTcZYuyI6Jx4WBhcg==",
+      "version": "1.59.0",
+      "resolved": "https://registry.npmjs.org/@algolia/ingestion/-/ingestion-1.59.0.tgz",
+      "integrity": "sha512-Fa38s1mHgoaLCT117sfJ6P78rtxUt93CYxBYpq1VOIcslaF+cH+1h5uikAPsKfxLnsuEDZHiBiaI6eNPTsQMRA==",
       "license": "MIT",
       "dependencies": {
-        "@algolia/client-common": "5.19.0",
-        "@algolia/requester-browser-xhr": "5.19.0",
-        "@algolia/requester-fetch": "5.19.0",
-        "@algolia/requester-node-http": "5.19.0"
+        "@algolia/client-common": "5.59.0",
+        "@algolia/requester-browser-xhr": "5.59.0",
+        "@algolia/requester-fetch": "5.59.0",
+        "@algolia/requester-node-http": "5.59.0"
       },
       "engines": {
         "node": ">= 14.0.0"
       }
     },
     "node_modules/@algolia/monitoring": {
-      "version": "1.19.0",
-      "resolved": "https://registry.npmjs.org/@algolia/monitoring/-/monitoring-1.19.0.tgz",
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-        "@algolia/requester-node-http": "5.19.0"
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-      "integrity": "sha512-0XavAZbNJ5sDrCbkpWL8mia0o5WPOd2YGtxrEiZkBK9FjLppIUK2TgxK6qGD2P3hUXTJNNPVibrerKcx5WkR1g==",
+      "version": "5.2.6",
+      "resolved": "https://registry.npmjs.org/webpack-dev-server/-/webpack-dev-server-5.2.6.tgz",
+      "integrity": "sha512-HNLRmamRvVavZQ+avceZifmv8hmdUjg43t6MI4SqJDwFdW7RPQwH5vzGhDRZSX59SgfbeHhLnq3g+uooWo7pVw==",
       "license": "MIT",
       "dependencies": {
-        "@types/bonjour": "^3.5.9",
-        "@types/connect-history-api-fallback": "^1.3.5",
-        "@types/express": "^4.17.13",
-        "@types/serve-index": "^1.9.1",
-        "@types/serve-static": "^1.13.10",
-        "@types/sockjs": "^0.3.33",
-        "@types/ws": "^8.5.5",
+        "@types/bonjour": "^3.5.13",
+        "@types/connect-history-api-fallback": "^1.5.4",
+        "@types/express": "^4.17.25",
+        "@types/express-serve-static-core": "^4.17.21",
+        "@types/serve-index": "^1.9.4",
+        "@types/serve-static": "^1.15.5",
+        "@types/sockjs": "^0.3.36",
+        "@types/ws": "^8.5.10",
         "ansi-html-community": "^0.0.8",
-        "bonjour-service": "^1.0.11",
-        "chokidar": "^3.5.3",
+        "bonjour-service": "^1.2.1",
+        "chokidar": "^3.6.0",
         "colorette": "^2.0.10",
-        "compression": "^1.7.4",
+        "compression": "^1.8.1",
         "connect-history-api-fallback": "^2.0.0",
-        "default-gateway": "^6.0.3",
-        "express": "^4.17.3",
+        "express": "^4.22.1",
         "graceful-fs": "^4.2.6",
-        "html-entities": "^2.3.2",
-        "http-proxy-middleware": "^2.0.3",
-        "ipaddr.js": "^2.0.1",
-        "launch-editor": "^2.6.0",
-        "open": "^8.0.9",
-        "p-retry": "^4.5.0",
-        "rimraf": "^3.0.2",
-        "schema-utils": "^4.0.0",
-        "selfsigned": "^2.1.1",
+        "http-proxy-middleware": "^2.0.9",
+        "ipaddr.js": "^2.1.0",
+        "launch-editor": "^2.14.1",
+        "open": "^10.0.3",
+        "p-retry": "^6.2.0",
+        "schema-utils": "^4.2.0",
+        "selfsigned": "^5.5.0",
         "serve-index": "^1.9.1",
         "sockjs": "^0.3.24",
         "spdy": "^4.0.2",
-        "webpack-dev-middleware": "^5.3.4",
-        "ws": "^8.13.0"
+        "webpack-dev-middleware": "^7.4.2",
+        "ws": "^8.18.0"
       },
       "bin": {
         "webpack-dev-server": "bin/webpack-dev-server.js"
       },
       "engines": {
-        "node": ">= 12.13.0"
+        "node": ">= 18.12.0"
       },
       "funding": {
         "type": "opencollective",
         "url": "https://opencollective.com/webpack"
       },
       "peerDependencies": {
-        "webpack": "^4.37.0 || ^5.0.0"
+        "webpack": "^5.0.0"
       },
       "peerDependenciesMeta": {
         "webpack": {
@@ -18708,10 +19232,40 @@
         }
       }
     },
+    "node_modules/webpack-dev-server/node_modules/define-lazy-prop": {
+      "version": "3.0.0",
+      "resolved": "https://registry.npmjs.org/define-lazy-prop/-/define-lazy-prop-3.0.0.tgz",
+      "integrity": "sha512-N+MeXYoqr3pOgn8xfyRPREN7gHakLYjhsHhWGT3fWAiL4IkAt0iDw14QiiEm2bE30c5XX5q0FtAA3CK5f9/BUg==",
+      "license": "MIT",
+      "engines": {
+        "node": ">=12"
+      },
+      "funding": {
+        "url": "https://github.com/sponsors/sindresorhus"
+      }
+    },
+    "node_modules/webpack-dev-server/node_modules/open": {
+      "version": "10.2.0",
+      "resolved": "https://registry.npmjs.org/open/-/open-10.2.0.tgz",
+      "integrity": "sha512-YgBpdJHPyQ2UE5x+hlSXcnejzAvD0b22U2OuAP+8OnlJT+PjWPxtgmGqKKc+RgTM63U9gN0YzrYc71R2WT/hTA==",
+      "license": "MIT",
+      "dependencies": {
+        "default-browser": "^5.2.1",
+        "define-lazy-prop": "^3.0.0",
+        "is-inside-container": "^1.0.0",
+        "wsl-utils": "^0.1.0"
+      },
+      "engines": {
+        "node": ">=18"
+      },
+      "funding": {
+        "url": "https://github.com/sponsors/sindresorhus"
+      }
+    },
     "node_modules/webpack-dev-server/node_modules/ws": {
-      "version": "8.18.0",
-      "resolved": "https://registry.npmjs.org/ws/-/ws-8.18.0.tgz",
-      "integrity": "sha512-8VbfWfHLbbwu3+N6OKsOMpBdT4kXPDDB9cJk2bJ6mh9ucxdlnNvH1e+roYkKmN9Nxw2yjz7VzeO9oOz2zJ04Pw==",
+      "version": "8.21.3",
+      "resolved": "https://registry.npmjs.org/ws/-/ws-8.21.3.tgz",
+      "integrity": "sha512-201TZ/kPWxoPr/OKWjquZR1SWKXcvxdH+e1xrx89b3YbmzLMFCLfnaG1HFIgWzJOEWZ7MvpK++odZufgYR50Rw==",
       "license": "MIT",
       "engines": {
         "node": ">=10.0.0"
@@ -18788,81 +19342,36 @@
       }
     },
     "node_modules/webpackbar": {
-      "version": "6.0.1",
-      "resolved": "https://registry.npmjs.org/webpackbar/-/webpackbar-6.0.1.tgz",
-      "integrity": "sha512-TnErZpmuKdwWBdMoexjio3KKX6ZtoKHRVvLIU0A47R0VVBDtx3ZyOJDktgYixhoJokZTYTt1Z37OkO9pnGJa9Q==",
+      "version": "7.0.0",
+      "resolved": "https://registry.npmjs.org/webpackbar/-/webpackbar-7.0.0.tgz",
+      "integrity": "sha512-aS9soqSO2iCHgqHoCrj4LbfGQUboDCYJPSFOAchEK+9psIjNrfSWW4Y0YEz67MKURNvMmfo0ycOg9d/+OOf9/Q==",
       "license": "MIT",
       "dependencies": {
-        "ansi-escapes": "^4.3.2",
-        "chalk": "^4.1.2",
+        "ansis": "^3.2.0",
         "consola": "^3.2.3",
-        "figures": "^3.2.0",
-        "markdown-table": "^2.0.0",
         "pretty-time": "^1.1.0",
-        "std-env": "^3.7.0",
-        "wrap-ansi": "^7.0.0"
+        "std-env": "^3.7.0"
       },
       "engines": {
         "node": ">=14.21.3"
       },
       "peerDependencies": {
+        "@rspack/core": "*",
         "webpack": "3 || 4 || 5"
-      }
-    },
-    "node_modules/webpackbar/node_modules/emoji-regex": {
-      "version": "8.0.0",
-      "resolved": "https://registry.npmjs.org/emoji-regex/-/emoji-regex-8.0.0.tgz",
-      "integrity": "sha512-MSjYzcWNOA0ewAHpz0MxpYFvwg6yjy1NG3xteoqz644VCo/RPgnr1/GGt+ic3iJTzQ8Eu3TdM14SawnVUmGE6A==",
-      "license": "MIT"
-    },
-    "node_modules/webpackbar/node_modules/markdown-table": {
-      "version": "2.0.0",
-      "resolved": "https://registry.npmjs.org/markdown-table/-/markdown-table-2.0.0.tgz",
-      "integrity": "sha512-Ezda85ToJUBhM6WGaG6veasyym+Tbs3cMAw/ZhOPqXiYsr0jgocBV3j3nx+4lk47plLlIqjwuTm/ywVI+zjJ/A==",
-      "license": "MIT",
-      "dependencies": {
-        "repeat-string": "^1.0.0"
       },
-      "funding": {
-        "type": "github",
-        "url": "https://github.com/sponsors/wooorm"
-      }
-    },
-    "node_modules/webpackbar/node_modules/string-width": {
-      "version": "4.2.3",
-      "resolved": "https://registry.npmjs.org/string-width/-/string-width-4.2.3.tgz",
-      "integrity": "sha512-wKyQRQpjJ0sIp62ErSZdGsjMJWsap5oRNihHhu6G7JVO/9jIB6UyevL+tXuOqrng8j/cxKTWyWUwvSTriiZz/g==",
-      "license": "MIT",
-      "dependencies": {
-        "emoji-regex": "^8.0.0",
-        "is-fullwidth-code-point": "^3.0.0",
-        "strip-ansi": "^6.0.1"
-      },
-      "engines": {
-        "node": ">=8"
-      }
-    },
-    "node_modules/webpackbar/node_modules/wrap-ansi": {
-      "version": "7.0.0",
-      "resolved": "https://registry.npmjs.org/wrap-ansi/-/wrap-ansi-7.0.0.tgz",
-      "integrity": "sha512-YVGIj2kamLSTxw6NsZjoBxfSwsn0ycdesmc4p+Q21c5zPuZ1pl+NfxVdxPtdHvmNVOQ6XSYG4AUtyt/Fi7D16Q==",
-      "license": "MIT",
-      "dependencies": {
-        "ansi-styles": "^4.0.0",
-        "string-width": "^4.1.0",
-        "strip-ansi": "^6.0.0"
-      },
-      "engines": {
-        "node": ">=10"
-      },
-      "funding": {
-        "url": "https://github.com/chalk/wrap-ansi?sponsor=1"
+      "peerDependenciesMeta": {
+        "@rspack/core": {
+          "optional": true
+        },
+        "webpack": {
+          "optional": true
+        }
       }
     },
     "node_modules/websocket-driver": {
-      "version": "0.7.4",
-      "resolved": "https://registry.npmjs.org/websocket-driver/-/websocket-driver-0.7.4.tgz",
-      "integrity": "sha512-b17KeDIQVjvb0ssuSDF2cYXSg2iztliJ4B9WdsuB6J952qCPKmnVq4DyW5motImXHDC1cBT/1UezrJVsKw5zjg==",
+      "version": "0.7.5",
+      "resolved": "https://registry.npmjs.org/websocket-driver/-/websocket-driver-0.7.5.tgz",
+      "integrity": "sha512-ZL2+3c7kMBdIRCMz6l8jQMHyGVxj+UL+xVk74Ombiciboca8rHa15L86B19E5oh1pL9Ii/uj54gtsIrZGMo6zA==",
       "license": "Apache-2.0",
       "dependencies": {
         "http-parser-js": ">=0.5.1",
@@ -18974,12 +19483,6 @@
         "url": "https://github.com/chalk/strip-ansi?sponsor=1"
       }
     },
-    "node_modules/wrappy": {
-      "version": "1.0.2",
-      "resolved": "https://registry.npmjs.org/wrappy/-/wrappy-1.0.2.tgz",
-      "integrity": "sha512-l4Sp/DRseor9wL6EvV2+TuQn63dMkPjZ/sp9XkghTEbV9KlPS1xUsZ3u7/IQO4wxtcFB4bgpQPRcR3QCvezPcQ==",
-      "license": "ISC"
-    },
     "node_modules/write-file-atomic": {
       "version": "3.0.3",
       "resolved": "https://registry.npmjs.org/write-file-atomic/-/write-file-atomic-3.0.3.tgz",
@@ -19013,6 +19516,36 @@
         }
       }
     },
+    "node_modules/wsl-utils": {
+      "version": "0.1.0",
+      "resolved": "https://registry.npmjs.org/wsl-utils/-/wsl-utils-0.1.0.tgz",
+      "integrity": "sha512-h3Fbisa2nKGPxCpm89Hk33lBLsnaGBvctQopaBSOW/uIs6FTe1ATyAnKFJrzVs9vpGdsTe73WF3V4lIsk4Gacw==",
+      "license": "MIT",
+      "dependencies": {
+        "is-wsl": "^3.1.0"
+      },
+      "engines": {
+        "node": ">=18"
+      },
+      "funding": {
+        "url": "https://github.com/sponsors/sindresorhus"
+      }
+    },
+    "node_modules/wsl-utils/node_modules/is-wsl": {
+      "version": "3.1.1",
+      "resolved": "https://registry.npmjs.org/is-wsl/-/is-wsl-3.1.1.tgz",
+      "integrity": "sha512-e6rvdUCiQCAuumZslxRJWR/Doq4VpPR82kqclvcS0efgt430SlGIk05vdCN58+VrzgtIcfNODjozVielycD4Sw==",
+      "license": "MIT",
+      "dependencies": {
+        "is-inside-container": "^1.0.0"
+      },
+      "engines": {
+        "node": ">=16"
+      },
+      "funding": {
+        "url": "https://github.com/sponsors/sindresorhus"
+      }
+    },
     "node_modules/xdg-basedir": {
       "version": "5.1.0",
       "resolved": "https://registry.npmjs.org/xdg-basedir/-/xdg-basedir-5.1.0.tgz",
@@ -19043,19 +19576,10 @@
       "integrity": "sha512-a4UGQaWPH59mOXUYnAG2ewncQS4i4F43Tv3JoAM+s2VDAmS9NsK8GpDMLrCHPksFT7h3K6TOoUNn2pb7RoXx4g==",
       "license": "ISC"
     },
-    "node_modules/yaml": {
-      "version": "1.10.2",
-      "resolved": "https://registry.npmjs.org/yaml/-/yaml-1.10.2.tgz",
-      "integrity": "sha512-r3vXyErRCYJ7wg28yvBY5VSoAF8ZvlcW9/BwUzEtUsjvX/DKs24dIkuwjtuprwJJHsbyUbLApepYTR1BN4uHrg==",
-      "license": "ISC",
-      "engines": {
-        "node": ">= 6"
-      }
-    },
     "node_modules/yocto-queue": {
-      "version": "1.1.1",
-      "resolved": "https://registry.npmjs.org/yocto-queue/-/yocto-queue-1.1.1.tgz",
-      "integrity": "sha512-b4JR1PFR10y1mKjhHY9LaGo6tmrgjit7hxVIeAmyMw3jegXR4dhYqLaQF5zMXZxY7tLpMyJeLjr1C4rLmkVe8g==",
+      "version": "1.2.2",
+      "resolved": "https://registry.npmjs.org/yocto-queue/-/yocto-queue-1.2.2.tgz",
+      "integrity": "sha512-4LCcse/U2MHZ63HAJVE+v71o7yOdIe4cZ70Wpf8D/IyjDKYQLV5GD46B+hSTjJsvV5PztjvHoU580EftxjDZFQ==",
       "license": "MIT",
       "engines": {
         "node": ">=12.20"
diff --git a/package.json b/package.json
index 72eef41..9d4213f 100644
--- a/package.json
+++ b/package.json
@@ -14,21 +14,21 @@
     "write-heading-ids": "docusaurus write-heading-ids"
   },
   "dependencies": {
-    "@docusaurus/core": "^3.7.0",
-    "@docusaurus/faster": "^3.7.0",
-    "@docusaurus/preset-classic": "^3.7.0",
-    "@mdx-js/react": "^3.1.0",
+    "@docusaurus/core": "^3.10.2",
+    "@docusaurus/faster": "^3.10.2",
+    "@docusaurus/preset-classic": "^3.10.2",
+    "@mdx-js/react": "^3.1.1",
     "clsx": "^2.1.1",
     "hast-util-is-element": "^3.0.0",
     "prism-react-renderer": "^2.4.1",
-    "react": "^19.0.0",
-    "react-dom": "^19.0.0",
+    "react": "^19.3.0",
+    "react-dom": "^19.3.0",
     "rehype-katex": "^7.0.1",
     "remark-math": "^6.0.0"
   },
   "devDependencies": {
-    "@docusaurus/module-type-aliases": "^3.7.0",
-    "@docusaurus/types": "3.7.0"
+    "@docusaurus/module-type-aliases": "^3.10.2",
+    "@docusaurus/types": "^3.10.2"
   },
   "browserslist": {
     "production": [
diff --git a/src/css/custom.css b/src/css/custom.css
index 3bafe4a..83d7739 100644
--- a/src/css/custom.css
+++ b/src/css/custom.css
@@ -27,12 +27,21 @@
     /*--ifm-color-primary-lighter: #32d8b4;*/
     /*--ifm-color-primary-lightest: #4fddbf;*/
 
-    --ifm-color-primary: #bd93f9; /* dracula purple */
-    --ifm-color-primary-dark: #ffb86c; /* dracula orange */
-    --ifm-color-primary-darker: #ff79c6; /* dracula pink */
-    --ifm-color-primary-darkest: #ff5555; /* dracula red */
-    --ifm-color-primary-light: #50fa7b; /* dracula green */
-    --ifm-color-primary-lighter: #f1fa8c; /* dracula yellow */
-    --ifm-color-primary-lightest: #8be9fd; /* dracula cyan */
+    /*--ifm-color-primary: #bd93f9; !* dracula purple *!*/
+    /*--ifm-color-primary-dark: #ffb86c; !* dracula orange *!*/
+    /*--ifm-color-primary-darker: #ff79c6; !* dracula pink *!*/
+    /*--ifm-color-primary-darkest: #ff5555; !* dracula red *!*/
+    /*--ifm-color-primary-light: #50fa7b; !* dracula green *!*/
+    /*--ifm-color-primary-lighter: #f1fa8c; !* dracula yellow *!*/
+    /*--ifm-color-primary-lightest: #8be9fd; !* dracula cyan *!*/
+
+    --ifm-color-primary: #c6a0f6; /* catppuccin purple */
+    --ifm-color-primary-dark: #f5a97f; /* catppuccin orange */
+    --ifm-color-primary-darker: #f5bde6; /* catppuccin pink */
+    --ifm-color-primary-darkest: #ed8796; /* catppuccin red */
+    --ifm-color-primary-light: #a6da95; /* catppuccin green */
+    --ifm-color-primary-lighter: #eed49f; /* catppuccin yellow */
+    --ifm-color-primary-lightest: #8bd5ca; /* catppuccin cyan */
+
     --docusaurus-highlighted-code-line-bg: rgba(0, 0, 0, 0.3);
 }