>>11369708

Within the confines of the given axioms, yes.The Field axioms for instance:

>0 =/= 1

>commutativity of addition/multiplication

>distributivity

>associativity

>existence of an additive inverse

>existence of a multiplicative inverse

>existence of additive/multiplicative identities

>closure under defined operations

There are many more axioms like the axioms of vector spaces, group axioms, ring axioms, lie axioms, axioms of "X" algebraic structure, axioms of set theory, ect. Mainly, how axioms are determined are arbitrary to an extent, but their consequences are very real for applied sciences, the application of group theory to chemistry/physics comes to mind as one of the most eminent examples.