# 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 if and only if $\struct {S, \circ}$ is not a finite structure.

## Also known as

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