Re: are Real Numbers evil? The answer(?).

Both newsgroups sci.math & comp.theory are fine to post to; ignore
those who say it isn't an appropriate question. You're basically
talking about the vices of limits. You could, in theory, have just Q
(the rationals, and mapable to Z, the integers). Physics simulations
and any other computer-based simulation will use IEEE754 numbers of the
form (+/- x * 2^-y). While, due to hardware limitations, x is in Z mod
2^52 and y is in Z mod 2^11, it seems that you have no complaints about
integers which are unbounded, limits tending to +/- inf. If so, then
your complaints are with irrationals only and not limits. Yes, then,
all of math is still possible without irrational elements.

Just as (most of) math uses +inf and -inf not as numerical values but
as limits, so too can you treat Pi or any other irrational as a limit
and not as an element. Instead of Z with only 2 limits (-inf, +inf), Q
will have 2^|Z| limits because we can concatenate the |Q|-length binary
prefix x (where x's bit1!= i's bit1, x's bit2!= j's bit2, etc for Q's
elements i,j,k,..) with a |Z|-length binary suffix y of arbitrary
construction (2^|Z| suffices). [Pedantic note: countably-infinite =
aleph-nought = |Q| = |Z|. |R| = 2^aleph-nought]

I partially agree with you: if +inf, -inf are not elements in the
number system, then I feel out of love for symmetry that other limits
of Q should not be. However, I disagree with you because I feel that
since other limits of Q are in R, then so too should +inf and -inf be
considered (irrational) elements in R. I would much prefer _all_
limits of Q to be in R instead of _no_ limits of Q in R. I abhor
partial-lists of limits being exalted with membership in R.

Claudio Grondi wrote:
> > I would have tried sci.math. comp.theory is for people who worry about
> > things like program correctness, etc.
> From my up to now experience I suppose,
> that there is no appropriate newgroup for
> what I am asking for. My first thought was,
> that comp.theory might be the best one
> to get attention from people who might
> eventually know what I am trying to get
> from the "symptoms" of how I ask for it.
> It seems, that this assumption was wrong.
>
>
> Claudio
>
> "Brandon J. Van Every" <mylastnameruntogether@xxxxxxxxxxxxxxxxx> schrieb im
> Newsbeitrag news:Sgqne.14048$w21.10394@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> > Claudio Grondi wrote:
> >
> > >Currently it appears to me, that it is not
> > >possible to talk here about 3D without
> > >using for it a real number based coordinate
> > >system approach, so I posted to the wrong
> > >newsgroup asking what I have asked for.
> > >
> > >
> > I would have tried sci.math. comp.theory is for people who worry about
> > things like program correctness, etc.
> >
> > --
> > Cheers, www.indiegamedesign.com
> > Brandon Van Every Seattle, WA
> >
> > "The pioneer is the one with the arrows in his back."
> > - anonymous entrepreneur

.

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