Cardinality of R^2

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September 7th 2009, 06:56 PM
math.dj

Cardinality of R^2

Show that cardinality of R^2 is cardinal number of continumm
September 7th 2009, 07:08 PM
ThePerfectHacker

Quote:

Originally Posted by math.dj

Show that cardinality of R^2 is cardinal number of continumm

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

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