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


> There is another possible approach that you might be interested in.

I have taken a look at http://www.math.psu.edu/simpson/sosoa/chapter1.pdf .
Even if it seems to be very close to what I am interested in,
it's not easy to read for me. So I need probably at least
more time until I can say how it fits to what I am looking for.

Claudio


<tchow@xxxxxxxxxxxxx> schrieb im Newsbeitrag
news:42a07210$0$573$b45e6eb0@xxxxxxxxxxxxxxxxxxxxxxxxxxxx
> In article <3gab9rFatcpjU1@xxxxxxxxxxxxxx>,
> Claudio Grondi <claudio.grondi@xxxxxxxxxx> wrote:
> >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.
>
> There is another possible approach that you might be interested in. It
does
> not address your concerns as directly as Fredkin's approach does, because
> some real numbers and limits are admitted. But the rough idea is that
only
> "computable" real numbers are allowed---those that can be described in a
> finite, concrete manner. I am referring to doing mathematics in the
system
> known as RCA_0. See http://www.math.psu.edu/simpson/sosoa and in
particular
> the "front matter and chapter one":
>
> http://www.math.psu.edu/simpson/sosoa/chapter1.pdf
>
> The advantage of this approach is that you can carry over a lot of
> standard mathematics unchanged, rather than having to reinvent everything
> from scratch. At the same time you eliminate many of the vague worries
> that many people have about all those intangible and seeming unphysical
> real numbers floating around.
>
>
> --
> Tim Chow tchow-at-alum-dot-mit-dot-edu
> The range of our projectiles---even ... the artillery---however great,
will
> never exceed four of those miles of which as many thousand separate us
from
> the center of the earth. ---Galileo, Dialogues Concerning Two New
Sciences


.

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