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Prove f(y) = y for every real number y

  1. May 8, 2016 #1
    A function f: R->R is a continuous function such that f(q) = q for every rational number q.
    Prove f(y) = y for every real number y.

    I know every irrational number is the limit to a sequence of rational numbers. But I not sure how to prove f(y) = y for every real number y. Any ideas?
  2. jcsd
  3. May 8, 2016 #2


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    2016 Award

    Staff: Mentor

    I moved your thread to our homework forums.

    You can use exactly that property about limits, together with continuity.
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