Wikipedia says "Today ZFC is the standard form of axiomatic set theory and as such is the most common foundation of mathematics."
What my parenthetical comment that you quoted meant to say (for anyone that was not familiar with it) is thaz ZFC is not some joke, or obscure set of axioms or something irrelevant. Without this remark I thought my comment read that way.
I hope you will agree that ZFC is simply "standard math" - even if its axioms are not referenced explicitly by many working mathematicians.
If this statement requires further refinement let me know. Obviously I'm not a mathematician!
Certainly, ZFC is not a pathological constructed example. When a mathematician looks for a foundational set of axioms, ZFC is THE standard choice. It is, and has been, for the last ~90 years at least.
My point was that foundational mathematics is rarely touched upon by a lot of normal pure mathematics (say number theory, field extension, graph theory).
Interestingly, I believe a lot of people actually dislike the axiom of choice. They find it to be way to 'complex' when compared to the other axioms. It is a lot like euler's 5-th axiom (2 straight lines with the same direction are equidistant everywhere). Interestingly in that case, removing the axiom led to spherical and hyperbolic geometry.
What my parenthetical comment that you quoted meant to say (for anyone that was not familiar with it) is thaz ZFC is not some joke, or obscure set of axioms or something irrelevant. Without this remark I thought my comment read that way.
I hope you will agree that ZFC is simply "standard math" - even if its axioms are not referenced explicitly by many working mathematicians.
If this statement requires further refinement let me know. Obviously I'm not a mathematician!