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Math Help - Analysis

  1. #1
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    Analysis

    By constructing an appropriate one-to-one, onto function, prove and C= U {-, } have the same cardinality.
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  2. #2
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    Quote Originally Posted by boardinfanatic89 View Post
    By constructing an appropriate one-to-one, onto function, prove and C= U {-, } have the same cardinality.
    Let f(0) = -infinity, f(1) = infinity, f(n) = n - 2 for each positive integer n > 1. Let f(x) = x for all other x. Then f bijects R onto C.
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  3. #3
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    Would it be possible to remove f(n) = n - 2 for each positive integer n > 1 and just have f(x)=x for all x in R?
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  4. #4
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    oh nevermind, you need it so that it covers values 0 and 1. Got it, thanks.
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