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Discontinuity

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For a value , let = (the limit from the left) and = (the limit from the right).

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If = = , the function is continuous at .

If = ≠ , the function has a removable discontinuity at .

If ≠ , and both values are finite, the function has a jump discontinuity at .

If ≠ , and one or both values is infinite, the function has an infinite discontinuity at . This is also called an essential discontinuity.

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Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA

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