After a few years of university mathematics I just realised that I do not really know the difference between an axiom and a definition. With some "research" on the interwebs (mathexchange, wiki). I think that axioms are definitions that build the foundation of a Theory.
E.g. we have group axioms because we build a theory on them. But they are nothing else than a definition and we can check if some object satisfies the axioms/definition to be a group.
Lets look at continuity. Its a definition that says when we call a function continuous. We can check if that is the case or not. Its not called an axiom because we first need to define other things to get to continuity, like topology or metric spaces. There can be multiple equivalent definitions, which is the case with continuity.
What do you think? Is that a somewhat accurate understanding of the terms?
