Re: A Guide for Cantor Cranks

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Article #817

#817

From: James Burns
Date: Thu, 24 Mar 2011 14:08

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Albrecht wrote:
> On 24 Mrz., 10:31, William Hughes
> <wpihug...@gmail.com> wrote:

>>Absolute piffle.  There is no reason that defining the
>>existence of the limit of finite ratios means that you
>>have to define either infinite quantities, or the ratio
>>of infinite quantities.
>
> So you admit that an infinite decimal number has crucial
> other properties than a finite decimal number? You admit
> that a number like 3.1415... is crucial different from a
> number like 0.75? But you insist that the "behaviour" of
> a number like 3.1415... should be like the "behaviour" of
> a number like 0.75?
>
> The axioms behind this view are silly.

If I am not mistaken, there is only one axiom that
distinguishes infinite decimal numbers (real numbers)
from finite decimal numbers (rational numbers, or close
enough for our purposes).

< For every non-empty set of real numbers, if it has
< an upper bound, then it has a least upper bound.

Upper bound and least upper bound are defined in the
expected ways:

Upper bound of set A == a real number greater than or
equal to every element of A

Least upper bound of set A == an upper bound of A
less than or equal to every upper bound of A

I just wanted to be sure:
do you find this axiom silly?

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From: James Burns <burns.87@osu.edu>
Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science
Subject: Re: A Guide for Cantor Cranks
Date: Thu, 24 Mar 2011 10:08:01 -0400
Organization: Ohio State University
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