On Fri, 07 Jul 2000, John Hasler wrote:
> Buddha Buck writes:
> > Are "1/100 Dollars" and "1/64 Dollars" considered the same "commodity" or
> > different "commodities"?
>
> Your broker may quote you prices in "1/64 Dollars" but he will always bill
> you in "1/100 Dollars". You will never have to record a transaction in
> "1/64 Dollars".
That is correct. I think folks may be confusing "commodities" and "prices".
They are fundamentally different.
With a commodity (something tangible that you can actually see and measure)
you are only concerned with "how much" and "of what". For example, "two"
"bushels of wheat". Let's call that pair a "pile". Now "piles" come in
various "sizes" and are of various materials (corn, beans, money), the
"commodity".
When you talk about a "price", you are referring to a rate of exchange.
A pile of this can be exchanged for a different sized pile of that.
We need to know the size of this pile and the size of that pile as well as
what commodity this is and that is.
A pile of 199 pennies can be exchanged for a pile of 64 lemon drops.
Now, in addition to the above mentioned properties, we also need to know the
smallest recognizable change in the size of a pile or price.
Since we require that we be able to represent that amount exactly, we must
linearly map the "size" onto the rational numbers. This implies that we must
include the exact reciprocal of this smallest unit in the scaling factor.
Now, for convenience, it is useful to make the scaling factor either just
this reciprocal or the radix multiple of it (unless the radix is odd)
The denominator of an amount because it is always a known constant. If we
apply a uniform policy in assigning scaling factors, it will be a global
constant. We need the scaling factor because it is the "exchange rate" used
to convert to printable units.
However, this is a common property of every value in this denomination and,
like the denominator, need not be stored with the individual values.
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