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

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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