>>12250990warning, brainlet understanding here, but these are my thoughts
it sounds obvious that if you have a set of things, you can pick out a single element. however, to be precise, you have to give an algorithm on how to do this. axiom of choice allows you to assume such an algorithm exists without specifying it. this is ok 99.99% of the time. however, the study of formal systems makes one wonder if you can always invoke the axiom of choice, because you have results like the Godel's incompleteness theorem. to me, axiom of choice is extremely suspect, even if it is ok most of the time
