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[TI] Compact: Add theorem 5.3

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Janis Hutz
2025-11-01 16:29:11 +01:00
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semester3/ti-compact/parts/04_computability.tex
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@@ -41,3 +41,6 @@ Since $M$ is a Turing Machine in the canonical ordering of all Turing Machines,
This however leads to a contradiction, as $w_i \in L_\text{diag} \Longleftrightarrow d_{ii} = 0 \Longleftrightarrow w_i \notin L(M_i)$. This however leads to a contradiction, as $w_i \in L_\text{diag} \Longleftrightarrow d_{ii} = 0 \Longleftrightarrow w_i \notin L(M_i)$.
In other words, $w_i$ is in $L_\text{diag}$ if and only if $w_i$ is not in $L(M_i)$, which contradicts our statement above. In other words, $w_i$ is in $L_\text{diag}$ if and only if $w_i$ is not in $L(M_i)$, which contradicts our statement above.
\setLabelNumber{theorem}{3}
\inlinetheorem $L_\text{diag} \notin \mathcal{L}_{RE}$

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semester3/ti-compact/ti-compact.pdf
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