Integers under Addition form Monoid

From ProofWiki
Jump to navigation Jump to search

Theorem

The set of integers under addition $\struct {\Z, +}$ forms a monoid.


Proof

Follows directly from Integers under Addition form Abelian Group.

By definition, an abelian group is a group.

Also by definition, a group is a monoid.

Hence the result.

$\blacksquare$


Sources