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