Thursday, 17 November 2016

analysis - Show that the function f:mathbbQtomathbbQ is continuous

Let αR be an irrational number. Show that the function f:QQ 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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