Re: bijection of R: R <--> Rx.....xR

On 7 Sep 2005 10:21:28 -0700, "Timothy Golden
http://www.BandTechnology.com"; <tttpppggg@xxxxxxxxx> wrote:

>Does anyone reject this method on philosophical grounds?
>The digits are merely a representation of a real number,
>not the real number itself. A value (a) and (b) in the reals
>would seem more valid, and a function defined mathematically:
> c = f ( a, b ).

First, it seem like _you_ are wrongly rejecting something
on philosophical grounds: Although it turns out it doesn't
quite solve the problem, if it did solve the problem there
would be nothing wrong with defining a function f(a,b) in
terms of the decimal digits.

>This thing you guys are doing is sort of a three tape Turing solution.
>Yes it works but where is the purity?
>How about a swirl where
> t = c
> r = c d
>where t is theta and r is radius.
>now a = r cos t
>and b = r sin t
>Within a delta related to d there will be a range of c that matches for
>any a and b.
>If more accuracy is needed then drop d.

First, I don't follow your definition at all. But more important,
it seems clear that you're _not_ defining a function! You say do
this, then you get a _range_ of c, if more accuracy is required
do something else...

To define a function f(a,b) you need to say exactly what f(a,b)
_is_ (which the definition in terms of digits does!), not what
it might be, or what it is approximately.

>Does this approach work for 3D?
>I don't see it.
>
>-Tim


************************

David C. Ullrich
.

Relevant Pages

  • Re: bijection of R: R <--> Rx.....xR
    ... David C. Ullrich wrote: ... > on philosophical grounds: Although it turns out it doesn't ... > terms of the decimal digits. ... > it seems clear that you're _not_ defining a function! ...
    (sci.math)
  • Re: bijection of R: R <--> Rx.....xR
    ... Does anyone reject this method on philosophical grounds? ... The digits are merely a representation of a real number, ... A value and in the reals ...
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  • Re: Math errors in python
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