continuous function
continuous function A function from one partially ordered set to another having the property, roughly speaking, that least upper bounds are preserved. A function f : S → T
is said to be continuous if, for every directed subset X of S, f maps the least upper bound of X to the least upper bound of the image of X under f. Continuous functions are significant in denotational semantics since they correspond to the requirement that a computational process produces arbitrarily close approximations to the final output, given arbitrarily close approximations to the total input.
A continuous function f(x) has no breaks or instantaneous changes in value. In the hierarchy of mathematical functions the smoothest are those, such as sin x, cos x, that can be differentiated any number of times, always producing a continuous function.
is said to be continuous if, for every directed subset X of S, f maps the least upper bound of X to the least upper bound of the image of X under f. Continuous functions are significant in denotational semantics since they correspond to the requirement that a computational process produces arbitrarily close approximations to the final output, given arbitrarily close approximations to the total input.
A continuous function f(x) has no breaks or instantaneous changes in value. In the hierarchy of mathematical functions the smoothest are those, such as sin x, cos x, that can be differentiated any number of times, always producing a continuous function.
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continuous function