David and Pat, (01)
DL> Presumably you also suggest two mappings: numbers <-> measures,
> and measures <-> quantity values. (02)
PH> I would actually just have measures and values... (03)
DL> I do not see the utility of the concept of "measure".
> It does not seem to be used in practice. (04)
I agree with Pat. The concept of 'measure' is very widely used.
For example, "1 inch" and "2.54 cm" represent exactly the same
measure, but they use different numbers and units. (05)
DL> Trivially there is a difference between a total function and
> a partial function -- how can this be if a function is just
> a set of pairs? (06)
I agree that Pat should have mentioned the two sets, domain and
range (AKA codomain), from which the elements of the pairs were
taken. (07)
I would also quibble with the claim that a function *is* a set
of pairs. I would prefer to say that a function is a mapping
between two sets. That mapping could be specified by a set of
pairs (extensionally) or by a rule (intensionally), which for
any element of the domain determines the corresponding element
of the range. For infinite sets, all specifications must be
intensional. (08)
For the distinction between extensions and intensions, see the
following excerpt by Alonzo Church: (09)
http://jfsowa.com/logic/alonzo.htm (010)
John Sowa (011)
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