For a value , let = (the limit from the left) and = (the limit from the right).
If L- = L+ = , the function is continuous at .
If L- = L+, the function has a removable discontinuity at .
If L-L+, and both values are finite, the function has a jump discontinuity at .
If L-L+, 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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