Number is an abstraction. What is an abstraction? It is a definition for a set of things by stating what is common to all things considered to be in that set.

Number is an abstraction. What is an abstraction? It is a definition for a set of things by stating what is common to all things considered to be in that set. "1" is the set of all things which have exactly one element. It is an abstraction for all such things. What does it mean to "have one element"? I think that's a more difficult question. Maybe it should be an axiom?