Re: Decimal versus binary arithmetic was Re: J4 -

Robert wrote:

> The ideal numeration base is an irrational called phi or golden ratio,
which is 1.61803...
> The only digits are 0 and 1, which makes it ideal for computers. One
would expect 'our'
> integers to produce infinately repeating fractions while irrational
numbers produce
> terminated fractions. Not so. In phinary, EVERY number can be
represented exactly in a
> finite string of 0s and 1s, including e, pi and square root of 2. That's
a very valuable
> attribute. For more on this, see:

In a finite string of 0s and 1s of length n 2^n different values can
be be represented. Regardless of what those representable values may
be there will always be another number that is not in that set of
values, in fact there will still be an infinite number of
unrepresented values.

Just because pi, e and root2 can be represented exactly does not mean
that "EVERY number can be represented exactly".