# Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Closure

< Abstract Algebra | Group Theory | Group | Definition of a Group

< Abstract Algebra | Group Theory | Group | Definition of a Group

Let G be a group with binary operation $\ast$

- $\forall \;a,b\in G:a\ast b\in G$

- If
*a*,*b*are in G, a $\ast$ b is in G.

- G has to be a group
- Both
*a*and*b*have to be elements of G. - $\ast$ has to be the binary operation of G
- The converse is not necessary true:
*a*$\ast$*b*is in G does not mean*a*or*b*must be in G.