Re: Element of?

From: Eckard Blumschein (blumschein_at_et.uni-magdeburg.de)
Date: 11/10/04 

Date: Wed, 10 Nov 2004 16:56:50 +0100

On 11/10/2004 3:31 PM, Will Twentyman wrote:
> Eckard Blumschein wrote:
>> As a layman I wonder if the basic meanings of all symbols used in axioms
>> of set theory have already been completely and unambiguously clarified.
>
> No. The axioms frequently serve to *help* clarify the meanings of the
> symbols. Also, any grammar rules *help* clarify the meanings.
> Ultimately, however, the meanings only exist unambiguously for a model
> of the axioms/symbols.

A mathematics that is not just a self-satisfying game has to be
carefully fitted into the whole knowledge of menkind. This requires at
first properly chosen most elementary basics. The Atoms of mathematics
are not the axioms but what one intends to express for instance with the
symbol for "element of".

> I have no idea what this is supposed to mean. Real and rational numbers
> are no more "uncertain" than integers.

If physicists and engineers prefer integers, they often do so because
these genuine numbers are absolutely precise. Calculation with reals or
more precisely rationals always depends on the chosen accuracy.

>
>> Given, zero does not exist as a rational number.
>
> Zero *is* a rational number. What made you think it is not?

I gave several reasons in de.sci.mathematics
Let me add a further one:
Zero is supposed to be a neutral number without any sign. Can you
imagine to divide a by b and yield a result without sign?

>
>> Given, the concept of real numbers covers zero just in case of the
>> potential infinity.
>
> Huh? What do you mean by "covers zero" and "potential infinity"?

As did Weyl, I consider a continuum a sauce.
The term potential infinity was introduced by Aristoteles and means
infinity is a fiction outside the wealth of numbers. There is actually
no infinite number.

>> Is there any justification for including or excepting a rational or real
>> zero in physics?
>
> I thought we were talking about math, which is a tool used in physics.

I respect mathematics, but I am an engineer who demands flawless tools.

>> Couldn't reals be interpreted as integers divided by an denominator of
>> infinite size? I would conclude from that: Reals are of quite different
>> quality.
>
> You can't have a denominator of infinite size, under any normal
> interpretation. You think the reals of "quite different quality" from
> *what*?

The entity of reals as a sauce is quite different from the notion of a
number.

What are you referring to with IZ, IQ,
> IR, and IC?

Sorry for my awkward letters. I meant integer, rational, real, and
complex numbers.

Eckard

Relevant Pages

  • Two worlds complementing each other
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    (sci.math)
  • Re: infinity
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    (sci.math)
  • Re: Calculus XOR Probability
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    (sci.math)
  • Re: Another naive question - limts are meant for not crossing or not reaching?
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    (sci.math)
  • Re: .999... ?= 1
    ... I do not throw away zero. ... The axioms of such a system cannot be consistent, ... > approximate reals. ...
    (sci.math)
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