Definition:Order of Structure/Infinite Structure

Definition
Let $\struct {S, \circ}$ be an algebraic structure. Let the underlying set $S$ of $\struct {S, \circ}$ be infinite.

Then $\struct {S, \circ}$ is an infinite structure.

That is, $\struct {S, \circ}$ is an infinite structure $\struct {S, \circ}$ is not a finite structure.

Also known as
An infinite structure can also be described as an algebraic structure of infinite order.

Also see

 * Definition:Finite Structure