# 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 $$f$$ is said to be continuous at a point $$n$$ if for any positive $$\epsilon$$ there exists an $$x$$ such that for all real $$|l|<x, \space |f(n+l)-f(n)|<\epsilon$$

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