Double Math

Group in Math , Definitions and Examples-Double Math:-

Definition: A non-empty set G having binary operation “*” (say) is called group in math if it satisfies the following axioms:

  • Closure Property w.r.t “*

i.e, a\ast b\in G\;\;\;\;\;\;\;\forall\;a,b\in G

  • Associative Law w.r.t “*

(a\ast b)\ast c=a\ast(b\ast c)\;\;\;\;\;\;:\;\forall\;a,b,c\in G.

  • Identity element exist.

There is identity element e in G such that

a\ast e=e\ast a=a\;\;\;\;\;\;\;\;\forall\;a\in G.

  • Inverse of each element exist.

For each a\in G, there is an a^{-1}\in\;G such that

you can also check semi group and monoid