Re: Relative Cardinality


David Kastrup wrote:
> Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx> writes:
>
> > In article <1121961944.900842.252120@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > mueckenh@xxxxxxxxxxxxxxxxx wrote:
> >
> >> because sqrt(2) does not exist in my sense. That is a consequence
> >> of the fact that it has not a periodic sequence of digits. You
> >> always compare a finite seqence of digits with another finite
> >> sequence of digits. But sqrt(2) is not among them.
> >
> > One can compare the continued fraction representations of sqrt(2)
> > with arbitrary rationals to determine their relative size,
>
> Oh good grief. Just square the rational in question and compare the
> resulting enumerator with two times the resulting denominator. If it
> is larger, the fraction is larger than sqrt(2). If it is smaller, the
> fraction is smaller than sqrt(2). If both are equal, you have a
> problem.

Not if you only have a finite amount of memory available. If every
particle in the universe contains a decimal place for the rational
number, there's no way to calculate its square (since there will be,
roughly, twice as many decimal places).

WM doesn't define a rational number as a number of the form a/b,
either; he insists on having decimal places until it repeats.

This is why I've kept on asking WM how he can compute anything in this
system; it seems to only allow representation of numbers, not
manipulation of numbers. This makes it rather useless ...

--- Christopher Heckman

.

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