Proving f is continuous

4. Consider the function f : R ? R, f(x) = ?x?, given by discarding the decimal
part of x: f(x) = max {y ? Z | y ? x}. For example, ?5.8? = 5 and ??2.3? =
?3. Find all points at which f is not continuous and prove this fact. Prove that
f is continuous at all other points.

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