[EMAIL PROTECTED] said:
> In between two bank balances there are a finite number number of other
> balances, therefore they _can_ be represented by the set of integers.
> This reasoning is the root of my suggestion to allow restricting
> allowable values of some variables to integers.
The number of rationals with a denominator of N between the two rationals
A/N and B/N is finite. i.e. the number of bank balances between two other
balances is finite because the denominator is fixed. Hence, they can be
represented by a single integer, but ONLY if the denominator is known (or
if a multiple of the denominator is known).
If I'm not mistaken, one of the reasons for Bill's proposal being as
so abstract is that it may be unreasonable to think that we can come up
with a denominator that will be a multiple of all other quantity
denominators. For any currency amount, it's probably reasonable to say
that any denominator would be a multiple of 1, 2 or 5 and hence 10^n
would be a reasonable denominator (we wouldn't need to store "10", just
the exponent). However, for quantities, we probably can't enumerate all
the possible denominators, hence a rational representation my very well
be necessary.
Jason D Rennie www.ai.mit.edu/~jrennie/
MIT: (617) 253-5339 [EMAIL PROTECTED]
MITRE: (781) 271-7249 [EMAIL PROTECTED]
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