Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Having only real values: having as its codomain the set of real numbers or a subset thereof.
Etymologies
Sorry, no etymologies found.
Examples

There are many examples in the literature defining a vector (vector field) as a triple of real numbers (realvalued functions) which transform in a certain way under certain coordinate changes.
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

As I said above, gij is not the metric tensor, or a tensor at all, but a set of realvalued function specified for a local coordinate system (gij are also the matrix elements in the matrix representation – in those coordinates – of the metric tensor).
Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element

The sketchiness of an individual is measured, like the skewness of any given realvalued variable, by the combination of several dimensions of behavior.

The sketchiness of an individual is measured, like the skewness of any given realvalued variable, by the combination of several dimensions of behavior  communication based on technicality, obfuscation, ambiguity, tonality, diversion, digression, and ratio of chocolate chips to dough.

The values of a bivalent quantity, for instance, form a set with two members; the values of a realvalued quantity form a set with the structure of the real numbers.

We can also represent simple realvalued random variables operatortheoretically.

In fact, these are only the special cases of realvalued plausibility measures.

And so on for all of the infinitely many equivalent reformulations of the problem (in terms of the fourth, fifth, ¦ power of the length, and indeed in terms of every nonzero realvalued exponent of the length).

There is a formal analogy between classical and quantum fields: field values are attached to spacetime points where these values are realvalued in the case of classical fields and operatorvalued in the case of quantum fields.

The notion of arbitrary set grew in the late 19th century from developments in analysis, somewhat in the way that the concept of arbitrary realvalued function had grown earlier in the century.
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