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steelphantom
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Homework Statement
Let f(x) = 1 for rational numbers x and f(x) = 0 for irrational numbers. Show that f is discontinuous at every x in R.
Homework Equations
Definition of continuity.
The Attempt at a Solution
I want to find a sequence (x_n) that converges to x_0 but that x_n is rational for even n, and irrational for odd n. This will show that (f(x_n)) cannot converge, since it will alternate between 0 and 1, and thus f is discontinuous. My problem is that I can't think of a sequence that does this!
Thanks for any help.