Rational Numbers under Addition form Monoid
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Theorem
The set of rational numbers under addition $\struct {\Q, +}$ forms a monoid.
Proof
Follows directly from Rational Numbers under Addition form Infinite Abelian Group.
By definition, an abelian group is a group.
Also by definition, a group is a monoid.
Hence the result.
$\blacksquare$
Sources
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.1$: Monoids