Over an interval, at domain points, function {continuous function} limits can equal range values. All polynomials are continuous functions. At points, if two functions are continuous, their sums, products, and quotients are continuous.
Over an interval, at domain points, function {discrete function} limits can not equal range values. Functions can have values only at a finite number of points. Finite strings can represent finite discrete point sets, so discrete functions can map finite strings onto finite strings.
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Date Modified: 2022.0225