Saltus Functions

This section introduces two mathematical functions that work like switches. Unlike most of the Excel functions (such as sine), which deliver a result value from an original value with no surprises, the saltus functions recognize only two result values: 0 and 1. Depending on the amount of the original value, they toggle between 0 and 1. The DELTA() function only recognizes one instance for which it returns 1. Otherwise, it always returns 0. The GESTEP() function, however, continuously toggles between 0 and 1, when the original value reaches or crosses a fixed minimum (a threshold).

The Dirac delta function δ(x) is the mathematical ancestor of these Excel functions. Like the two Excel functions, it belongs to the saltus functions. ...

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