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If x is between two consecutive integers such that n ≤ x < n + 1, then the greatest integer function [x] maps x to the largest integer smaller than x so that [x] = n.
(i) If x is approaching -2 from above, that means x > -2. As x gets closer to -2, we essentially have -2 < x < -1, so that [x] will approach
(ii) However, if x is approaching -2 from below, then x < -2, so that [x] = -3. In other words
Because the one-sided limits do not match, the two-sided limit
(iii) -2.4 lies between -3 and -2, so