# Definition:Order of Structure/Finite Structure

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## Contents

## Definition

Let $\struct {S, \circ}$ be an algebraic structure.

Let the underlying set $S$ of $\struct {S, \circ}$ be finite.

Then $\struct {S, \circ}$ a **finite structure**.

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

## Also known as

A **finite structure** can also be described as an algebraic structure **of finite order**.

## Also see

## Sources

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): $\S 4.4$. Gruppoids, semigroups and groups

- 1974: Thomas W. Hungerford:
*Algebra*... (previous) ... (next): $\text{I}$: Groups: $\S 1$ Semigroups, Monoids and Groups