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## Main Question or Discussion Point

Hello,

In my abstract algebra class, my teacher really stresses that when you show that a set is a group by satisfying the axioms of a group (law of combination, associativity, identity element, inverse elements) these axioms MUST be proved in order.

This makes some amount of sense to me, as some axoims use other axioms in their definitions, but why must associativity be proved before the existence of the identity element or inverses? Thank you.

In my abstract algebra class, my teacher really stresses that when you show that a set is a group by satisfying the axioms of a group (law of combination, associativity, identity element, inverse elements) these axioms MUST be proved in order.

This makes some amount of sense to me, as some axoims use other axioms in their definitions, but why must associativity be proved before the existence of the identity element or inverses? Thank you.