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In article <MPG.1e9f1d5a48675f0898abfa@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> David R Tribble said:
> > Virgil said:
> > >> I have never seen "Orlow's amazing H-Riffic Number System" either.
> > >
> >
> > Tony Orlow wrote:
> > > 1. 0 is a real number
> > > 2. If x is a real number, then 2^x and 2^-x are real numbers.
> > >
> > > You have seen it, and now you see it again, and you've seen other
> > > versions of
> > > it as well.
> >
> > You omitted the part where you claim that all reals can be derived by
> > recursively applying rule 2.
> >
> > They can't. An uncountable number of reals are never derived.
> > For example, applying rule 2 repeatedly will never result in even a
> > simple number like 3.
> >
> > But please, oh please, prove me wrong.
> >
> >
>
> I wish I could give you a good answer. Hopefully, at some point, I can get to
> implementing the H-riffics on the computer
No "real number system", nor anything requiring infinitely many objects
can be "implemented on a computer" as long as computers are limited to
finitely many states.
One can approximate such systems usefully, as has been done, but never
more that approximate them.
Anyone familiar with computer science should know better.
, and make it do my survey for me
> so
> I can derive rules once the intuition is established, but these gradal-type
> numbers are difficult. Right now, I cannot exactly tell you the bit string
> corresponding to 3.
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