Definition:Order of Structure/Infinite Structure

Definition
Let $\left({S, \circ}\right)$ be an algebraic structure. Let the underlying set $S$ of $\left({S, \circ}\right)$ be infinite.

Then $\left({S, \circ}\right)$ is an infinite structure.

That is, $\left({S, \circ}\right)$ is an infinite structure $\left({S, \circ}\right)$ 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