>>11601106whatever you want
it's just that if you define too much, your definitions will contradict each other
A collective set of assumptions and definitions form a mathematical theory, that theory's assumptions and deifinitons have logical consequences that are always true where their assumptions and definitons are true. these are known as theorems and lemmas
mathematics, as a whole, is inconsistent and has no universal assumptions or definitions. high level math is more about the abstract studying of assumptions and the logical conclusions they lead to, this is known as inductive reasoning.
reverse math is an interesting field btw as a side note. you work backwards. you see some properties, or some structure, and ask "what assumptions and definitions not only allow for this structure/property, but give rise to it". It's a surprisingly difficult field. It's also the only mathematical field to my knowledge that is more-so deductive than inductive.
