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Math Help - cardinality of sets

  1. #1
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    cardinality of sets

    Is it true that \mathbb{|R|} < \mathbb{|R}^2|
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  2. #2
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    No. \mathbb{R} is equinumerous with (0,1); the bijection between these sets can be constructed using the tangent function on (-\pi/2,\pi/2). Similarly, \mathbb{R}^2 is equinumerous with (0,1)\times(0,1). Now, there is a bijection (0,1)\to(0,1)\times(0,1). See section 4 in this PDF document.
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