“There are many examples in the literature defining a vector (vector field) as a triple of real numbers (real-valued functions) which transform in a certain way under certain coordinate changes.”
“As I said above, gij is not the metric tensor, or a tensor at all, but a set of real-valued function specified for a local coordinate system (gij are also the matrix elements in the matrix representation – in those coordinates – of the metric tensor).”
“The sketchiness of an individual is measured, like the skewness of any given real-valued variable, by the combination of several dimensions of behavior.”
“The sketchiness of an individual is measured, like the skewness of any given real-valued 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 real-valued quantity form a set with the structure of the real numbers.”
“We can also represent simple real-valued random variables operator-theoretically.”
“In fact, these are only the special cases of real-valued 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 non-zero real-valued exponent of the length).”
“There is a formal analogy between classical and quantum fields: field values are attached to space-time points where these values are real-valued in the case of classical fields and operator-valued 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 real-valued function had grown earlier in the century.”
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