Let α∈R be an irrational number. Show that the function f:Q→Q is continuous, where f is given by f(x)=x for x<α and x+1 for x>α.
I'm not sure how to go about this, I've been trying to use the fact that every rational number has a sequence of irrationals converging to it, but it doesn't seem to go anywhere. Any help would be appreciated. Thanks!
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