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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