Monoid

An Algebraic Structure that has less Axioms than a Group because it doesn’t require an Inverse

Axioms

1. Closure: $a,b\in g⟹ab\in g$
2. Associativity: $a,b,c\in g⟹(ab)c=a(bc)$
3. Identity: $\exists i\text{ s.t. }\forall a\in g,ia=ai=a$