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## Homework Statement

Let f: R -> Z be the ceiling function defined by f(x) = ceil(x). Give a ε-δ proof that if a is a real number that is not an integer, then f is continuous at a.

## The Attempt at a Solution

I can prove that f(x) is not continuous at any integer. But i don't know how to prove this. I can do proofs for continuous functions, but I've never done one for a piece wise function. Any help would be awesome. Thanks.