Integers under Addition form Group

Theorem

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

Proof

From Integers under Addition form Abelian Group, $\struct {\Z, +}$ forms an abelian group.

An abelian group is a fortiori a group.

Hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): group
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): group