I find it most perplexing for how the definition of say, a set, defines itself. How does it become tangible? Where does it come from? Because, arbitrary definition seems more so like just saying "it just is", or "let it be so" without any axiom to ground it from which it may become literal.
Apologies, I don't know a lot of Math (and I'm not good at reading it either, so algebra eludes me visually) but it's troubled me of recent with regards to defining "something". All I keep finding is that "something", however arbitrary and abstract it may be, invariably requires an axiom to connect it with something else from which it may become real (literal).
I hope this question makes sense. I mean -- from what I understand, there should be an all defining axiom from which anything may occur (perhaps which one may find by traversing through other axioms, so on and so forth). Perhaps likewise for numbers too I suppose, I mean I assume that for them to simply be - for abstract quantities to be - that there must be some defining axiom, from which numbers just become.