The Banach-Tarski Paradox, non-measurable sets, continuous functions that map measurable sets to non-measurable sets, impossible-to-implement strategies with even more impossible results (the blog's link to the paper is broken, but this one works). And then there's the result that many well-orderings on the real numbers exist, but none of them can be constructed.
Do we take our math seriously enough to accept the things above? Why or why not? Where do we draw the line(s)?
(For those keeping score: all the things above use the axiom of choice)
Do we take our math seriously enough to accept the things above? Why or why not? Where do we draw the line(s)?
(For those keeping score: all the things above use the axiom of choice)
