Mathematics is seen a formally grown, logical system, that has features that are "discovered" rather than invented .. "Given some {X}, {Y} follows without question".
It is understood that one can tweak an axiom, the fifth posulate for example, and get a different logical ediface - a non Euclidean hyperbolic geometry in that case.
The ZFC "Axiom of Choice" has bearing on infinities and other things, including many proofs that depend on reduction by absurdity.
Mathematics is seen a formally grown, logical system, that has features that are "discovered" rather than invented .. "Given some {X}, {Y} follows without question".
However it rests(?) on Axiomatic foundations ..
Most famously: https://www.sfu.ca/~swartz/euclid.htm
It is understood that one can tweak an axiom, the fifth posulate for example, and get a different logical ediface - a non Euclidean hyperbolic geometry in that case.
The ZFC "Axiom of Choice" has bearing on infinities and other things, including many proofs that depend on reduction by absurdity.
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t...