theory, money-supplyWhat is the mathematical structure or object that represents the concept of money? Is it a real number, a function of time, a functional in a Hilbert space? Or more generally, is it a mapping from X to Y? If so, what are the spaces X and Y?
I'm not sure at all that this is a meaningful question. Why should there be one mathematical structure that represents the concept of money? Perhaps there's none. Perhaps there are several, depending on the context.
Here's one way of looking at it. I don't know if this is any use.
Money is a mapping from (X,X,time,space) to the set of rational numbers, where X is the set of saleable goods and services. It indicates at any one place in time and space how much of any one member of X is worth, relative to another.
So, for example:
f(Brent Crude Oil, WTI Crude Oil,2012-03-06 08:00:00,London spot oil market) $\approx$ 1.1586
Source: FT.com; prices WTI Crude US\$106.88/b. Brent Crude US\$123.83/b
But that only covers one of the roles of money - acting as a metric for the relative value of good. Money has several roles, and a very blurry definition. Or, to put it another way, it has multiple partially overlapping definitions.
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