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 Operations|binary operation]] $\ast$

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

Usage

1. Template:AnchorIf a, b are in G, a $\ast$ b is in G.

Notice

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