Maybe it was just because it was late, but while reading the comments following Mark Chu-Carroll's post on debating John Gabriel, I found this comment (#432):
[snip]
Reading "axiom of choice" now on Wikipedia...maybe that will help.
followed shortly thereafter by this comment (#433):
Reading "axiom of choice" now on Wikipedia...And now I wish I hadn't: Whatthefuck?!?!?!?! That's going to bother me for a long time...
[snip]
to be hysterically funny.
The axiom of choice is one of my favorite WTFs in pure mathematics since it's "intuitively obvious" (i.e., "of course I can pick an element from every non-empty set") and yet leads to bizarre results, such as sets of reals having a well ordering and the Banach-Tarski paradox (visit Irregular Webcomic for a decent informal explanation). Now, the follow up comment rightly noted that much of why the Banach-Tarski result seems "wrong" is because our physical intuitions about measures such as "volume" and "surface area" break down when talking about objects like the Menger sponge (which has infinite surface area and zero volume). But that doesn't mean there aren't times when math is just freaking weird.
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