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Definition: Suppose f is discontinuous at c. If either f(c+) or f(c-) does not exist, or both f(c+) and f(c-) exist but have different values, then c is an irremovable discontinuity because the discontinuity cannot be removed by redefining f at c. Here we used the notation that f(c+) is the right hand limit, and f(c-) is the left hand limit.
Source: Mathematical Analysis, second edition by Tom M. Apostol