Natural Numbers under Addition do not form Group/Corollary

Corollary to Natural Numbers under Addition do not form Group

The algebraic structure $\struct {\Z_{\ge 0}, +}$ consisting of the set of non-negative integers $\Z_{\ge 0}$ under addition $+$ does not form a subgroup of the additive group of integers.

Proof

By Natural Numbers are Non-Negative Integers, $\struct {\Z_{\ge 0}, +}$ and $\struct {\N, +}$ are the same (or if not exactly the same, at least isomorphic).

The result follows from Natural Numbers under Addition do not form Group.

$\blacksquare$

Sources

• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Exercise $\text{E i}$