# Group is not Empty

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## Theorem

## Proof

A group is defined as a monoid for which every element has an inverse.

Thus, as a group is already a monoid, it must *at least* have an identity, therefore can not be empty.

$\blacksquare$

## Sources

- 1968: Ian D. Macdonald:
*The Theory of Groups*... (previous) ... (next): $\S 1$: Some examples of groups