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

=Definition of Closure= Let G be a group with binary operation $$\ast$$


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

=Usage=
 * 1) If 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:
 * 5) a $$\ast$$ b is in G does not mean a or b must be in G.