real-valued

Adjective

Meaning

real valued (not comparable)

(mathematics) Used to describe a mathematical entity, like a function, that takes values from the real numbers (as opposed to, for instance, from the complex numbers).

real-valued (not comparable)

(mathematical analysis, of a function) Having only real values: having as its codomain the set of real numbers or a subset thereof.

Alternative names

real valued

Synonyms

Examples

A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Source: Internet

After the manipulations, the simplified result is still real-valued. Source: Internet

An important consequence is that every metric space admits partitions of unity and that every continuous real-valued function defined on a closed subset of a metric space can be extended to a continuous map on the whole space ( Tietze extension theorem ). Source: Internet

A uniformity compatible with the topology of a completely regular space X can be defined as the coarsest uniformity that makes all continuous real-valued functions on X uniformly continuous. Source: Internet

Fourier originally defined the Fourier series for real-valued functions of real arguments, and using the sine and cosine functions as the basis set for the decomposition. Source: Internet

A classical plane wave with imaginary amplitude would have a (real-valued) Poynting vector opposite the direction of propagation- the wave radiates negative energy. Source: Internet

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