Alex_Altair comments on Harry Potter and the Methods of Rationality discussion thread, part 8 - Less Wrong
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I had to check to be sure, but then saw others noted it: Raw ZF seems quite sufficient to prove its existence.
So even tossing Choice in the bin isn't enough to get rid of it.
EDIT: Perhaps this is math's revenge for you having tiled a hall in Hogwarts with pentagons. :)
But he didn't say regular pentagons. Pentagon tiles shown here. Also, he did say that Hogwarts has non-Euclidean geometry.
Actually, my understanding was that he said it didn't have geometry at all, only topology.