axiom

An axiom is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. It can also be thought as a proposition that is accepted true without justification.

Source.

If someone tells you that badgers are white, 200 feet tall, and glow in the dark, they're not even wrong about badgers: whatever they mean by badger, it isn't what you mean by badger. Similarly, if someone tells you that the natural numbers don't satisfy induction and also include \[-3\] and \[\frac{5}{7}\], then they're not even wrong about the natural numbers: whatever they mean by natural number, it isn't what you mean by natural number.

People think of axioms as laws you have to follow or true things you have to assume and I think neither of these perspectives is correct. It's more accurate to think of axioms as a way to agree that we're talking about the same thing.