Define h: R-> R by h(x) = { x^2, x is rational { 0, x is irrational Prove that h is not continous at c not equal to 0. Split the proof into two cases: one for c rational, the other for c irrational.
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Originally Posted by Sterwine Define h: R-> R by h(x) = { x^2, x is rational { 0, x is irrational Prove that h is not continous at c not equal to 0. Split the proof into two cases: one for c rational, the other for c irrational. Well if , then , s.t. and . So given a point , letting (for instance), will ensure that and . You can do a very similar thing for irrational.
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