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Thread: Cardinality of R^2

  1. September 7th 2009, 06:56 PM #1
    math.dj
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    Cardinality of R^2

    Show that cardinality of R^2 is cardinal number of continumm
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  2. September 7th 2009, 07:08 PM #2
    ThePerfectHacker
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    Quote Originally Posted by math.dj View Post
    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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