Re: Corrective interpretation of real numbers

guenther.vonKnakspott_at_gmx.de
Date: 01/27/05 

Date: 27 Jan 2005 10:36:53 -0800

Eckard Blumschein wrote:
> Do not get me wrong. If I mention that Weierstrass's notion of a
limit
> does never permit delta to be zero, I am fully aware of the fact that
> this notion is the decisive basis not merely for a most rigorous
picture
> but rather for something fundamentally different from Peirce's
> description: "A continuum is precisely that every part of which has
> parts". So I do not share the widespread lack of understanding. I
just
> would like to suggest a corrective interpretation of real numbers.
Let
> me exemplary explain why.
>
> As long as we neglect the potentiality of infinity, and we do so with
> great success, we cannot avoid some unreasonable consequences.
> - Let e.g. any number x cut IR. Then there is no consensus whether x
> belongs to the smaller or the larger numbers. For x=0, both IR+ and
IR-
> need a neutral element of addition and should offer the option of
> reunification.
> - Buridan's donkey is suffering starvation between two full
mangers
> because of lacking preference for the left or the right one.
> - "Correctness" demands to graphically represent |sign(x)|=0
like a
> singular point.
> - Practice would appreciate to be released from obligation to always
> carefully distinguish in IR between open and closed intervals just
for
> unspecified "mathematical" reasons even if such distinction does
> obviously not make any sense.
>
> Common sense provides the only reasonable elucidation and corrective
> interpretation of real numbers if applied before or after calculating
> with mathematics based on Weierstrass's notion as usual:
>
> Imagine delta equal to zero: Now, any single number x does not matter
> any more. Infinitely many are required as to change a function f(x)
by
> addition or removal of numbers. Singularities only belong to
> distributions. Equality of two irrational numbers tends to evade
> numerical examination. When mathematicians like Stifel and Weyl used
> profane terminology like fog or sauce as to express the essence of an
> untamed continuum, then perhaps they did know why.
>
> The alluded simple "external" reinterpretation can be used
without any
> scruples but with much ease and success as compared to hyperreal or
> surreal numbers in order to correct for unreasonable consequences of
the
> standard analysis.

Hello Blumschein here we go again. Why do you do this to yourself? Do
you derive any pleasure from being ridiculed and insulted? Do you not
get enough of that in the Kraut groups that you need to post at
sci.math to get more of the same? Or is it just to spice things up by
getting a dose in English? Face it Blumschein, nobody is going to go
and change mathematics for your sake. Regardless of how often and how
loud you whine. The fault lies with you, with your inabilities and your
shortcommings. Do you remember Donald G. Shead, a fellow engineer of
yours who kept whining about the advantages of the imperial system of
measures? Does the similarity of your plights make you feel any shame?