I honestly have a difficult time understanding the AC paradoxes, too. I recognize that it's totally necessary for many things (i.e. multidimensional integrals)

I honestly have a difficult time understanding the AC paradoxes, too. I recognize that it's totally necessary for many things (i.e. multidimensional integrals) and when it's consistent with a logical conclusion I have little trouble "seeing" it. Otherwise, though, not so much. I think it's interesting to see the connection between the AC and the Law of Excluded Middle which also causes paradoxical issues from time to time. http://en.wikipedia.org/wiki/Axiom_of_choice#Law_of_the_excluded_middle http://en.wikipedia.org/wiki/Axiom_of_choice#Law_of_the_excl...