What Would It Look Like?

Calculus Level 3

Does there exist a function that is continuous at all irrational points but not continuous at all rational points?

Definition (for this question): A function ff is said to be continuous at a point nn if for any positive ϵ\epsilon there exists an xx such that for all real l<x, f(n+l)f(n)<ϵ|l|<x, \space |f(n+l)-f(n)|<\epsilon

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