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docs/mathematik/mengenlehre/1_logik.mdx

@@ -287,143 +287,143 @@ Die tatsächliche semantische Äquivalenz lässt sich leicht durch aufstellen ei
 :::tip Wichtige semantische Äquivalenzen
 
 1. $$
-\begin{align*} 
+    \begin{align*}
-    \begin{aligned} 
+        \begin{aligned}
-        x \wedge y &\equiv y \wedge x\\
+            x \wedge y &\equiv y \wedge x\\
-        x \vee y &\equiv y \vee x\\
+            x \vee y &\equiv y \vee x\\
-        x \leftrightarrow y &\equiv y \leftrightarrow x 
+            x \leftrightarrow y &\equiv y \leftrightarrow x
-    \end{aligned}
+        \end{aligned}
-    &&\text{Kommutativität}
+        &&\text{Kommutativität}
-\end{align*}
+    \end{align*}
-$$
+    $$
 2. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned} 
+        \begin{aligned}
-        x \wedge (y \wedge z) &\equiv (x \wedge y) \wedge z\\
+            x \wedge (y \wedge z) &\equiv (x \wedge y) \wedge z\\
-        x \vee (y \vee z) &\equiv (x \vee y) \vee z\\
+            x \vee (y \vee z) &\equiv (x \vee y) \vee z\\
-        x \leftrightarrow (y \leftrightarrow z)
+            x \leftrightarrow (y \leftrightarrow z)
-        &\equiv (x \leftrightarrow y) \leftrightarrow z
+            &\equiv (x \leftrightarrow y) \leftrightarrow z
-    \end{aligned}
+        \end{aligned}
-    &&\text{Assoziativität}
+        &&\text{Assoziativität}
-\end{align*}
+    \end{align*}
-$$
+    $$
 3. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-        x \wedge (y \vee z) &\equiv (x \wedge y) \vee (x \wedge z)\\
+            x \wedge (y \vee z) &\equiv (x \wedge y) \vee (x \wedge z)\\
-        x \vee (y \wedge z) &\equiv (x \vee y) \wedge (x \vee z)
+            x \vee (y \wedge z) &\equiv (x \vee y) \wedge (x \vee z)
-    \end{aligned}
+        \end{aligned}
-    &&\text{Distributivität}
+        &&\text{Distributivität}
-\end{align*}
+    \end{align*}
-$$
+    $$
 4. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-        x \wedge (x \vee y) &\equiv x\\
+            x \wedge (x \vee y) &\equiv x\\
-        x \vee (x \wedge y) &\equiv x
+            x \vee (x \wedge y) &\equiv x
-    \end{aligned}
+        \end{aligned}
-    &&\text{Absorption}
+        &&\text{Absorption}
-\end{align*}
+    \end{align*}
-$$
+    $$
 5. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-        x \wedge x &\equiv x\\
+            x \wedge x &\equiv x\\
-        x \vee x &\equiv x
+            x \vee x &\equiv x
-    \end{aligned}
+        \end{aligned}
-    &&\text{Idempotenz}
+        &&\text{Idempotenz}
-\end{align*}
+    \end{align*}
-$$
+    $$
 6. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-        \neg(\neg x) &\equiv x\\
+            \neg(\neg x) &\equiv x\\
-        \neg(x \rightarrow y) &\equiv x \wedge \neg y\\
+            \neg(x \rightarrow y) &\equiv x \wedge \neg y\\
-        \neg(x \leftrightarrow y)
+            \neg(x \leftrightarrow y)
-        &\equiv \neg x \leftrightarrow y
+            &\equiv \neg x \leftrightarrow y
-        \equiv x \leftrightarrow \neg y
+            \equiv x \leftrightarrow \neg y
-    \end{aligned}
+        \end{aligned}
-    &&\text{Verneinung}
+        &&\text{Verneinung}
-\end{align*}
+    \end{align*}
-$$
+    $$
 7. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-        \neg(x \wedge y) &\equiv \neg x \vee \neg y\\
+            \neg(x \wedge y) &\equiv \neg x \vee \neg y\\
-        \neg(x \vee y) &\equiv \neg x \wedge \neg y
+            \neg(x \vee y) &\equiv \neg x \wedge \neg y
-     \end{aligned}
+         \end{aligned}
-    &&\text{De Morgan'sche Regeln}
+        &&\text{De Morgan'sche Regeln}
-\end{align*}
+    \end{align*}
-$$
+    $$
 8. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-           x \leftrightarrow y &\equiv (x \rightarrow y) \wedge (y \rightarrow x)\\
+               x \leftrightarrow y &\equiv (x \rightarrow y) \wedge (y \rightarrow x)\\
-           x \rightarrow y &\equiv \neg x \vee y\\
+               x \rightarrow y &\equiv \neg x \vee y\\
-           x \wedge y &\equiv \neg(\neg x \vee \neg y)\\
+               x \wedge y &\equiv \neg(\neg x \vee \neg y)\\
-           x \vee y &\equiv \neg(\neg x \wedge \neg y)
+               x \vee y &\equiv \neg(\neg x \wedge \neg y)
-    \end{aligned}
+        \end{aligned}
-    &&\text{Elimination}
+        &&\text{Elimination}
-\end{align*}
+    \end{align*}
-$$
+    $$
 9. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-        x \rightarrow y \equiv \neg y \rightarrow \neg x
+            x \rightarrow y \equiv \neg y \rightarrow \neg x
-    \end{aligned}
+        \end{aligned}
-    &&\text{Kontraposition}
+        &&\text{Kontraposition}
-\end{align*}
+    \end{align*}
-$$
+    $$
 10. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-       \neg f &\equiv w\\
+           \neg f &\equiv w\\
-       \neg w &\equiv f
+           \neg w &\equiv f
-    \end{aligned}
+        \end{aligned}
-    &&
+        &&
-\end{align*}
+    \end{align*}
-$$
+    $$
 11. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-       x \wedge \neg x &\equiv f\\
+           x \wedge \neg x &\equiv f\\
-       x \vee \neg x &\equiv w\\
+           x \vee \neg x &\equiv w\\
-       x \leftrightarrow \neg x &\equiv f
+           x \leftrightarrow \neg x &\equiv f
-    \end{aligned}
+        \end{aligned}
-    &&
+        &&
-\end{align*}
+    \end{align*}
-$$
+    $$
 12. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-       w \wedge x &\equiv x\\
+           w \wedge x &\equiv x\\
-       f \wedge x &\equiv f\\
+           f \wedge x &\equiv f\\
-       w \vee x &\equiv w\\
+           w \vee x &\equiv w\\
-       f \vee x &\equiv x
+           f \vee x &\equiv x
-    \end{aligned}
+        \end{aligned}
-    &&
+        &&
-\end{align*}
+    \end{align*}
-$$
+    $$
 13. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-       f \rightarrow x &\equiv w\\
+           f \rightarrow x &\equiv w\\
-       w \rightarrow x &\equiv x\\
+           w \rightarrow x &\equiv x\\
-       x \rightarrow f &\equiv \neg x\\
+           x \rightarrow f &\equiv \neg x\\
-       x \rightarrow w &\equiv w
+           x \rightarrow w &\equiv w
-    \end{aligned}
+        \end{aligned}
-    &&
+        &&
-\end{align*}
+    \end{align*}
-$$
+    $$
 14. $$
-\begin{align*}
+    \begin{align*}
-    \begin{aligned}
+        \begin{aligned}
-       f \leftrightarrow x &\equiv \neg x\\
+           f \leftrightarrow x &\equiv \neg x\\
-       w \leftrightarrow x &\equiv x
+           w \leftrightarrow x &\equiv x
-    \end{aligned}
+        \end{aligned}
-    &&
+        &&
-\end{align*}
+    \end{align*}
-$$
+    $$
 
 :::
 

docusaurus.config.js

@@ -1,14 +1,14 @@
 // @ts-check
 // Note: type annotations allow type checking and IDEs autocompletion
 
-const lightCodeTheme = require('prism-react-renderer/themes/github');
+import remarkMath from 'remark-math';
-const darkCodeTheme = require('prism-react-renderer/themes/dracula');
+import rehypeKatex from 'rehype-katex';
 
-const math = require('remark-math');
+const lightCodeTheme = require('prism-react-renderer').themes.github;
-const katex = require('rehype-katex');
+const darkCodeTheme = require('prism-react-renderer').themes.dracula;
 
 /** @type {import('@docusaurus/types').Config} */
-const config = {
+export default {
     title: 'Mathematik, Informatik und Programmierung',
     tagline: 'Mathematik und Informatik sind cool',
     url: 'https://www.niklas-birk.de',
@@ -38,8 +38,8 @@ const config = {
                 // docs: false,
                 docs: {
                   sidebarPath: require.resolve('./sidebars.js'),
-                  remarkPlugins: [math],
+                  remarkPlugins: [remarkMath],
-                  rehypePlugins: [katex],
+                  rehypePlugins: [rehypeKatex],
                 //   // Please change this to your repo.
                 //   // Remove this to remove the "edit this page" links.
                 //   // editUrl:
@@ -171,5 +171,3 @@ const config = {
         },
     ],
 };
-
-module.exports = config;

package.json

@@ -1,6 +1,6 @@
 {
   "name": "niklas-birk-blog",
-  "version": "0.1.0",
+  "version": "0.1.1",
   "private": true,
   "scripts": {
     "docusaurus": "docusaurus",
@@ -14,19 +14,20 @@
     "write-heading-ids": "docusaurus write-heading-ids"
   },
   "dependencies": {
-    "@docusaurus/core": "^2.4.1",
+    "@docusaurus/core": "^3.0.0",
-    "@docusaurus/preset-classic": "^2.4.1",
+    "@docusaurus/preset-classic": "^3.0.0",
-    "@mdx-js/react": "^1.6.22",
+    "@mdx-js/react": "^3.0.0",
     "clsx": "^1.2.1",
-    "hast-util-is-element": "^1.1.0",
+    "hast-util-is-element": "^3.0.0",
-    "prism-react-renderer": "^1.3.5",
+    "prism-react-renderer": "^2.1.0",
-    "react": "^17.0.2",
+    "react": "^18.2.0",
-    "react-dom": "^17.0.2",
+    "react-dom": "^18.2.0",
-    "rehype-katex": "^5.0.0",
+    "rehype-katex": "^7.0.0",
-    "remark-math": "^3.0.1"
+    "remark-math": "^6.0.0"
   },
   "devDependencies": {
-    "@docusaurus/module-type-aliases": "^2.1.0"
+    "@docusaurus/module-type-aliases": "^3.0.0",
+    "@docusaurus/types": "3.0.0"
   },
   "browserslist": {
     "production": [
@@ -41,6 +42,6 @@
     ]
   },
   "engines": {
-    "node": ">=16.14"
+    "node": ">=18.0"
   }
 }