In mathematical analysis, the Cauchy index is an integer associated to a real rational function over an interval.he integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French) are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (?1, ?2, ?3, ...). Viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... ?2, ?1, 0, 1, 2, ...}. For example, 65, 7, and ?756 are integers; 1.6 and 1 1/2 are not integers.

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