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

Closure:
a*b is in G if a, b are in Group G

# Definition of Closure

Let G be a group with binary operation ${\displaystyle \ast }$

${\displaystyle \forall \;a,b\in G:a\ast b\in G}$

# Usage

1. If a, b are in G, a ${\displaystyle \ast }$ b is in G.

# Notice

1. G has to be a group
2. Both a and b have to be elements of G.
3. ${\displaystyle \ast }$ has to be the binary operation of G
4. The converse is not necessary true:
1. a ${\displaystyle \ast }$ b is in G does not mean a or b must be in G.