Upgrade to Docusaurus 3.0
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@ -287,17 +287,17 @@ Die tatsächliche semantische Äquivalenz lässt sich leicht durch aufstellen ei
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:::tip Wichtige semantische Äquivalenzen
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:::tip Wichtige semantische Äquivalenzen
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1. $$
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1. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \wedge y &\equiv y \wedge x\\
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x \wedge y &\equiv y \wedge x\\
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x \vee y &\equiv y \vee x\\
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x \vee y &\equiv y \vee x\\
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x \leftrightarrow y &\equiv y \leftrightarrow x
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x \leftrightarrow y &\equiv y \leftrightarrow x
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\end{aligned}
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\end{aligned}
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&&\text{Kommutativität}
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&&\text{Kommutativität}
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\end{align*}
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\end{align*}
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$$
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$$
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2. $$
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2. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \wedge (y \wedge z) &\equiv (x \wedge y) \wedge z\\
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x \wedge (y \wedge z) &\equiv (x \wedge y) \wedge z\\
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x \vee (y \vee z) &\equiv (x \vee y) \vee z\\
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x \vee (y \vee z) &\equiv (x \vee y) \vee z\\
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@ -305,37 +305,37 @@ $$
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&\equiv (x \leftrightarrow y) \leftrightarrow z
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&\equiv (x \leftrightarrow y) \leftrightarrow z
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\end{aligned}
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\end{aligned}
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&&\text{Assoziativität}
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&&\text{Assoziativität}
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\end{align*}
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\end{align*}
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$$
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$$
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3. $$
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3. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \wedge (y \vee z) &\equiv (x \wedge y) \vee (x \wedge z)\\
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x \wedge (y \vee z) &\equiv (x \wedge y) \vee (x \wedge z)\\
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x \vee (y \wedge z) &\equiv (x \vee y) \wedge (x \vee z)
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x \vee (y \wedge z) &\equiv (x \vee y) \wedge (x \vee z)
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\end{aligned}
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\end{aligned}
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&&\text{Distributivität}
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&&\text{Distributivität}
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\end{align*}
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\end{align*}
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$$
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$$
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4. $$
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4. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \wedge (x \vee y) &\equiv x\\
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x \wedge (x \vee y) &\equiv x\\
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x \vee (x \wedge y) &\equiv x
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x \vee (x \wedge y) &\equiv x
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\end{aligned}
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\end{aligned}
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&&\text{Absorption}
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&&\text{Absorption}
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\end{align*}
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\end{align*}
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$$
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$$
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5. $$
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5. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \wedge x &\equiv x\\
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x \wedge x &\equiv x\\
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x \vee x &\equiv x
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x \vee x &\equiv x
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\end{aligned}
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\end{aligned}
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&&\text{Idempotenz}
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&&\text{Idempotenz}
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\end{align*}
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\end{align*}
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$$
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$$
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6. $$
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6. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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\neg(\neg x) &\equiv x\\
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\neg(\neg x) &\equiv x\\
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\neg(x \rightarrow y) &\equiv x \wedge \neg y\\
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\neg(x \rightarrow y) &\equiv x \wedge \neg y\\
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@ -344,19 +344,19 @@ $$
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\equiv x \leftrightarrow \neg y
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\equiv x \leftrightarrow \neg y
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\end{aligned}
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\end{aligned}
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&&\text{Verneinung}
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&&\text{Verneinung}
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\end{align*}
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\end{align*}
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$$
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$$
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7. $$
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7. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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\neg(x \wedge y) &\equiv \neg x \vee \neg y\\
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\neg(x \wedge y) &\equiv \neg x \vee \neg y\\
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\neg(x \vee y) &\equiv \neg x \wedge \neg y
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\neg(x \vee y) &\equiv \neg x \wedge \neg y
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\end{aligned}
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\end{aligned}
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&&\text{De Morgan'sche Regeln}
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&&\text{De Morgan'sche Regeln}
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\end{align*}
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\end{align*}
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$$
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$$
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8. $$
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8. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \leftrightarrow y &\equiv (x \rightarrow y) \wedge (y \rightarrow x)\\
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x \leftrightarrow y &\equiv (x \rightarrow y) \wedge (y \rightarrow x)\\
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x \rightarrow y &\equiv \neg x \vee y\\
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x \rightarrow y &\equiv \neg x \vee y\\
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@ -364,37 +364,37 @@ $$
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x \vee y &\equiv \neg(\neg x \wedge \neg y)
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x \vee y &\equiv \neg(\neg x \wedge \neg y)
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\end{aligned}
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\end{aligned}
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&&\text{Elimination}
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&&\text{Elimination}
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\end{align*}
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\end{align*}
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$$
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$$
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9. $$
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9. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \rightarrow y \equiv \neg y \rightarrow \neg x
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x \rightarrow y \equiv \neg y \rightarrow \neg x
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\end{aligned}
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\end{aligned}
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&&\text{Kontraposition}
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&&\text{Kontraposition}
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\end{align*}
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\end{align*}
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$$
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$$
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10. $$
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10. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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\neg f &\equiv w\\
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\neg f &\equiv w\\
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\neg w &\equiv f
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\neg w &\equiv f
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\end{aligned}
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\end{aligned}
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&&
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&&
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\end{align*}
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\end{align*}
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$$
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$$
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11. $$
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11. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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x \wedge \neg x &\equiv f\\
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x \wedge \neg x &\equiv f\\
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x \vee \neg x &\equiv w\\
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x \vee \neg x &\equiv w\\
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x \leftrightarrow \neg x &\equiv f
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x \leftrightarrow \neg x &\equiv f
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\end{aligned}
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\end{aligned}
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&&
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&&
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\end{align*}
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\end{align*}
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$$
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$$
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12. $$
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12. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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w \wedge x &\equiv x\\
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w \wedge x &\equiv x\\
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f \wedge x &\equiv f\\
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f \wedge x &\equiv f\\
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@ -402,10 +402,10 @@ $$
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f \vee x &\equiv x
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f \vee x &\equiv x
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\end{aligned}
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\end{aligned}
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&&
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&&
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\end{align*}
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\end{align*}
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$$
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$$
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13. $$
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13. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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f \rightarrow x &\equiv w\\
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f \rightarrow x &\equiv w\\
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w \rightarrow x &\equiv x\\
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w \rightarrow x &\equiv x\\
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@ -413,17 +413,17 @@ $$
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x \rightarrow w &\equiv w
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x \rightarrow w &\equiv w
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\end{aligned}
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\end{aligned}
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&&
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&&
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\end{align*}
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\end{align*}
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$$
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$$
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14. $$
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14. $$
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\begin{align*}
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\begin{align*}
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\begin{aligned}
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\begin{aligned}
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f \leftrightarrow x &\equiv \neg x\\
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f \leftrightarrow x &\equiv \neg x\\
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w \leftrightarrow x &\equiv x
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w \leftrightarrow x &\equiv x
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\end{aligned}
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\end{aligned}
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&&
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&&
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\end{align*}
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\end{align*}
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$$
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$$
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:::
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:::
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@ -1,14 +1,14 @@
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// @ts-check
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// @ts-check
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// Note: type annotations allow type checking and IDEs autocompletion
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// Note: type annotations allow type checking and IDEs autocompletion
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const lightCodeTheme = require('prism-react-renderer/themes/github');
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import remarkMath from 'remark-math';
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const darkCodeTheme = require('prism-react-renderer/themes/dracula');
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import rehypeKatex from 'rehype-katex';
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const math = require('remark-math');
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const lightCodeTheme = require('prism-react-renderer').themes.github;
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const katex = require('rehype-katex');
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const darkCodeTheme = require('prism-react-renderer').themes.dracula;
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/** @type {import('@docusaurus/types').Config} */
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/** @type {import('@docusaurus/types').Config} */
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const config = {
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export default {
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title: 'Mathematik, Informatik und Programmierung',
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title: 'Mathematik, Informatik und Programmierung',
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tagline: 'Mathematik und Informatik sind cool',
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tagline: 'Mathematik und Informatik sind cool',
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url: 'https://www.niklas-birk.de',
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url: 'https://www.niklas-birk.de',
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@ -38,8 +38,8 @@ const config = {
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// docs: false,
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// docs: false,
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docs: {
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docs: {
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sidebarPath: require.resolve('./sidebars.js'),
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sidebarPath: require.resolve('./sidebars.js'),
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remarkPlugins: [math],
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remarkPlugins: [remarkMath],
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rehypePlugins: [katex],
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rehypePlugins: [rehypeKatex],
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// // Please change this to your repo.
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// // Please change this to your repo.
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// // Remove this to remove the "edit this page" links.
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// // Remove this to remove the "edit this page" links.
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// // editUrl:
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// // editUrl:
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@ -171,5 +171,3 @@ const config = {
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},
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},
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],
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],
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};
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};
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module.exports = config;
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package-lock.json
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17170
package-lock.json
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25
package.json
25
package.json
@ -1,6 +1,6 @@
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{
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{
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"name": "niklas-birk-blog",
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"name": "niklas-birk-blog",
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"version": "0.1.0",
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"version": "0.1.1",
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"private": true,
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"private": true,
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"scripts": {
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"scripts": {
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"docusaurus": "docusaurus",
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"docusaurus": "docusaurus",
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"write-heading-ids": "docusaurus write-heading-ids"
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"write-heading-ids": "docusaurus write-heading-ids"
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},
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},
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"dependencies": {
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"dependencies": {
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"@docusaurus/core": "^2.4.1",
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"@docusaurus/core": "^3.0.0",
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"@docusaurus/preset-classic": "^2.4.1",
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"@docusaurus/preset-classic": "^3.0.0",
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"@mdx-js/react": "^1.6.22",
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"@mdx-js/react": "^3.0.0",
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"clsx": "^1.2.1",
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"clsx": "^1.2.1",
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"hast-util-is-element": "^1.1.0",
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"hast-util-is-element": "^3.0.0",
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"prism-react-renderer": "^1.3.5",
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"prism-react-renderer": "^2.1.0",
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"react": "^17.0.2",
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"react": "^18.2.0",
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"react-dom": "^17.0.2",
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"react-dom": "^18.2.0",
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"rehype-katex": "^5.0.0",
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"rehype-katex": "^7.0.0",
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"remark-math": "^3.0.1"
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"remark-math": "^6.0.0"
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},
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},
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"devDependencies": {
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"devDependencies": {
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"@docusaurus/module-type-aliases": "^2.1.0"
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"@docusaurus/module-type-aliases": "^3.0.0",
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"@docusaurus/types": "3.0.0"
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},
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},
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"browserslist": {
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"browserslist": {
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"production": [
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"production": [
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@ -41,6 +42,6 @@
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]
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]
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},
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},
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"engines": {
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"engines": {
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"node": ">=16.14"
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"node": ">=18.0"
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}
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}
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}
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}
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