(July 10, 2019 at 7:55 am)Jehanne Wrote:(July 10, 2019 at 4:55 am)polymath257 Wrote: Once you accept that there *is* a set of real numbers, then you can do the Cantor trick. But it is an *axiom* that there even exists an infinite set. Without that axiom (which the finitists reject), there may only be finite sets.
Without axioms, there is no mathematics.
Yes, precisely. So the question is *which* axioms. How do we choose the axioms? And it seems different people have different opinions on how to choose.
