"Bradd W. Szonye" <xxxxxx@szonye.com> writes:

> Marcin 'Qrczak' Kowalczyk wrote:
>> I would reject the concept of inexact integers ....
>
> While they seem silly for small integers, inexact integers make sense
> for huge values. For example, people often round huge integers to the
> nearest million or billion. An even better example: Avogadro's number is
> an integer, but it should not be represented as an exact integer,
> because its exact value is unknown.

What makes you think Avogadro's number is an integer?

It's the number of atoms in 12 grams of carbon-12, but it would be
quite an amazing coincidence if that turned out to be integral, if we
did have a sufficiently precise definition of the kilogram.  There is
of course an integral number of atoms in any sample at given moment in
time (*), but assuming there were an absolutely precise definition of
the kilogram, what makes you think that it should turn out so that
there are lumps of carbon that weigh *exactly* 12 grams?

Moreover, the kilogram isn't even specified to that precision, since
it is specified by an artifact, and the artifiact changes over time.
If you want a specification of the kilogram to that degree, it would
have to be some time-average of the mass of the standard kilogram, and
the result would of course then be that there aren't even an integral
number of atoms in the standard kilogram!

Oh, and that assertion I made that there are an integral number of
atoms in a sample at a moment in time: not really true.  After all,
the atoms are evaporating and condensing on to and off of the surface
of the sample all the time at an exceedingly high rate.  So high a
rate, in fact, that the width of the sample is relativistically
important now.  (Because, after all, we are talking about counting
*each* atom exactly.)  So if you want to talk about the number of
atoms in the sample, that also involves a necessary averaging of some
sort too.

Thomas