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## Homework Statement

For each [tex]a\in\mathbb{R}[/tex], find a function [tex]f[/tex] that is continuous at [tex]x=a[/tex] but discontinuous at all other points.

## The Attempt at a Solution

I guess I am not getting the question. I need to come up with a function, I was thinking of a piecewise defined one, half rational half irrational, which is continuous on one but not the other? Is this possible?

Thank you in advance