Real Numbers under Addition form Infinite Abelian Group

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $\R$ be the set of real numbers.

The structure $\struct {\R, +}$ is an infinite abelian group.


Proof

From Real Numbers under Addition form Group, $\struct {\R, +}$ is a group.

Then:

Real Addition is Commutative

and:

Real Numbers are Uncountably Infinite.

$\blacksquare$


Sources