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

  • #1
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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?
 

Answers and Replies

  • #2
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I moved your thread to our homework forums.

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

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