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

> 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

I an finite model there is no place for -inf and +inf and limits. Just
any distance, any direction any angle can be given by one value
out of the finite values making the model limited to a set where each
element can be explicitly specified. No need for limit values.

Claudio

"Navin Kumar" <navin.kumar@xxxxxxxxx> schrieb im Newsbeitrag
news:1117774969.137762.69730@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> 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
>


.

Relevant Pages

  • Re: Peanos space-filling curve
    ... >> A bijection between the unit interval and the unit square. ... >> Extend to irrationals by limits. ... The function is continuous at irrationals, ...
    (sci.fractals)
  • Re: Peanos space-filling curve
    ... >> A bijection between the unit interval and the unit square. ... >> Extend to irrationals by limits. ... The function is continuous at irrationals, ...
    (sci.math)
  • Re: Peanos space-filling curve
    ... > A bijection between the unit interval and the unit square. ... "extend to irrationals by limits" needs explanation, ...
    (sci.math)
  • Re: Peanos space-filling curve
    ... > A bijection between the unit interval and the unit square. ... "extend to irrationals by limits" needs explanation, ...
    (sci.fractals)
  • Re: integration problem
    ... to y by taking x as constant and with limits -inf to inf. ... Inner matrix dimensions must agree." ... Your term f*k*gis a matrix multiplication, ...
    (comp.soft-sys.matlab)