# Cardinality of R^2

• Sep 7th 2009, 06:56 PM
math.dj
Cardinality of R^2
Show that cardinality of R^2 is cardinal number of continumm
• Sep 7th 2009, 07:08 PM
ThePerfectHacker
Quote:

Originally Posted by math.dj
Show that cardinality of R^2 is cardinal number of continumm

$|\mathbb{R}\times \mathbb{R}| = |\mathbb{R}|\cdot |\mathbb{R}| = 2^{\aleph_0} \cdot 2^{\aleph_0} = 2^{\aleph_0 + \aleph_0} = 2^{\aleph_0}=|\mathbb{R}|$