Integers under Multiplication form Countably Infinite Commutative Monoid

From ProofWiki
Jump to navigation Jump to search

Theorem

The set of integers under multiplication $\left({\Z, \times}\right)$ is a countably infinite commutative monoid.


Proof

First we note that Integers under Multiplication form Monoid.

$\Box$


Then we have:

Commutativity

Integer Multiplication is Commutative.

$\Box$


Infinite

Integers are Countably Infinite.

$\blacksquare$


Sources