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