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jump discontinuity

noun Mathematics.

a discontinuity of a function at a point where the function has finite, but unequal, limits as the independent variable approaches the point from the left and from the right. Compare jump (def. 52).

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"Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity, there is no such jump; and because jump is missing in the world of quantity, it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate."

-Gregory Bateson

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