Typo in the first proof of Cantor's theorem (you got in vs not in mixed up in the second case).
I hadn't noticed before that Cantor's theorem and Russell's paradox were exactly the same argument. This makes me curious as to how Cantor failed to notice Russell's paradox.
Edit: It appears that Cantor actually did figure out that Cantor's theorem leads to things like Russell's paradox in 1899, two years before Russell did.
Thanks for the correction! I think the main impediment to noticing Russell's paradox was having the idea that something like that existed to be noticed.
I wouldn't normally link to a post from my math blog here, but it concerns a cute interpretation of Cantor's theorem that showed up when I was thinking about program equilibria at the April MIRI workshop, so I thought it might be of interest here (e.g. if you're trying to persuade a mathematically inclined friend of yours to attend a future workshop). A short proof of the undecidability of the halting problem falls out as a bonus.