bounded function

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bounded function

bounded function

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A real function f, defined on a domain S, is bounded (on S) if there is a number M such that, for all x in S, |f(x)| < M. The fact that, if f is continuous on a closed interval [a, b] then it is bounded on [a, b], is a property for which a rigorous proof is not elementary (see continuous function).

Subjects: Mathematics.

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