format updates

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Zheyuan Wu
2025-09-24 01:27:46 -05:00
parent e59ef423f3
commit 143d77e7f9
16 changed files with 401 additions and 79 deletions

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@@ -24,7 +24,8 @@ Given a set $S$, the power set of $S$, denoted $\mathscr{P}(S)$ or $2^S$, is the
Cardinality of $2^S$ is not equal to the cardinality of $S$.
Proof:
<details>
<summary>Proof of Cantor's Theorem</summary>
Assume they have the same cardinality, then $\exists \psi: S \to 2^X$ which is one-to-one and onto. (this function returns a subset of $S$)
@@ -38,7 +39,7 @@ If $b\in T$, then by definition of $T$, $b \notin \psi(b)$, but $\psi(b) = T$, w
If $b \notin T$, then $b \in \psi(b)$, which is also a contradiction since $b\in T$. Therefore, $2^S$ cannot have the same cardinality as $S$.
QED
</details>
### Back to Hankel's Conjecture