This might be a slightly silly question, apologies for that.
Anyways, I have been studying Linear Algebra and some Group Theory at University over the last few months and I started wondering why Axioms like the group axioms, vector space axioms etc are axioms, rather than just conditions that mathematical objects satisfy.
The reason I ask this is because the Group axioms especially, seem to me no different, in type, from say the conditions which a bijective function satisfies or the conditions an odd number satisfies.
So my main question is , why are group axioms, vector space axiom, inner product axioms, etc called axioms rather than simply conditions.
Any ideas will be appreciated.