(Section 1.5: Piecewise-Defined Functions; Limits and Continuity in Calculus) 1.5.12 fhas a jump discontinuityat a, or x=a±1) limx±a²fx()exists, and (call this limit L1) 2) limx±a+exists, but (call this limit L2) 3) limx±a²³limx±a+. (L1±L2) Therefore, the two-sided limit limx±adoes not exist. It is irrelevant how fais defined, or if it is at all. Example 2 and the greatest integer functiongave us jump discontinuities
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