piecewise
piecewise
English Definitions:
piecewise (Adverb)
In terms or by means of pieces; a piece at a time.
piecewise (Adverb)
Throughout separate parts, but not necessarily throughout the whole
Piecewise
In mathematics, a piecewise-defined function is a function which is defined by multiple subfunctions, each subfunction applying to a certain interval of the main function's domain. Piecewise is actually a way of expressing the function, rather than a characteristic of the function itself, but with additional qualification, it can describe the nature of the function. For example, a piecewise polynomial function: a function that is a polynomial on each of its subdomains, but possibly a different one on each. The word piecewise is also used to describe any property of a piecewise-defined function that holds for each piece but may not hold for the whole domain of the function. A function is piecewise differentiable or piecewise continuously differentiable if each piece is differentiable throughout its subdomain, even though the whole function may not be differentiable at the points between the pieces. In convex analysis, the notion of a derivative may be replaced by that of the subderivative for piecewise functions. Although the "pieces" in a piecewise definition need not be intervals, a function isn't called "piecewise linear" or "piecewise continuous" or "piecewise differentiable" unless the pieces are intervals.
Piecewise
In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself. A distinct, but related notion is that of a property holding piecewise for a function, used when the domain can be divided into intervals on which the property holds. Unlike for the notion above, this is actually a property of the function itself. A piecewise linear function (which happens to be also continuous) is depicted as an example.
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"piecewise." Kamus.net. STANDS4 LLC, 2024. Web. 29 Mar. 2024. <https://www.kamus.net/english/piecewise>.
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