Re: infinitely much - not infinitely many
From: Lee Rudolph (lrudolph_at_panix.com)
Date: 06/01/04
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Date: 1 Jun 2004 10:30:10 -0400
Eckard Blumschein <blumschein@et.uni-magdeburg.de> writes:
>While I do not intend offending anybody,
Amusement and contempt are not the same as offense. (For
that matter, intent and action are also distinct.)
>I would like to express serious
>doubts that Weierstrass and Cantor took the best choice in their
>definitions of numbers and infinity. Doesn't Buridans donkey still
>remind all mathematicians of their lacking understanding?
>
>I cannot imagine any justification
The limitations, or other defects, of your imagination
neither limit nor make defective the imaginations--and
other mental activities--of persons other than yourself.
>or the distinction between:
>uncountable and countable infinite. To my understanding
[repeat the above remark, substituting "understanding"
for "imagination"]
>the latter does
>not really make sense. One can never reach the infinite by counting.
Yes, and so...?
>David Hilbert desired:
>"Aus dem Paradies das Cantor uns schuf soll niemand uns vertreiben
>knnen". He failed in that.
>Experts of number theory are perhaps worst qualified as to comprehend
>that the infinite and the continuum on the hand and the notion of a
>number on the other hand mutually exclude each other.
There are examples of persons who are not "experts of number theory"
who are far worse "qualified as to comprehend" that particular bit
of bafflegam. I have my own opinion as to where one such example may
be found.
>I also question whether it makes sense to distinguish between a
>particular number in Q or IR and its immediate neighbourhood. To my
>understanding, any single number within a continuum does not have any
>weight as compared to its surroundings.
>
>Correspondingly every interval in Q or IR is an open one, no matter
>whether or not it has been declared closed. In Q as well as in IR all
>particular numbers including all natural ones are dispensable
>altogether. In other words, the natural numbers are not really
>constituents of Q or IR.
>
>Sensibly ruled by prudent poeple rather than narrow minded theoreticians
>Buridan's donkey does not suffer starvation because there is not at all
>a precise number zero in IR but infinitely much adjacent indiscriminably
>identical "number-like continuous stuff" (infinitely many numbers would
>not be the correct description).
Have you met John Morgan? I think you and he might profitably have
a meeting of the minds, out of which might issue the definitive
characterization of prudent people and true scientists.
>I am well aware of ridiculous attempts to attribute zero to IR+ as in
>case of numbers like 0.00001 or to IR- as in case of distributions which
>are imagined as an area below a ramp that rises to the right. Nothing
>besides a collection of outdated futile tenets justifies to arbitrary
>ascribe zero to either the left or the right.
>
>I am just suggesting to restrict numbers to the wealth of countables.
>You might calculate 1 minus 1 equals 0. However, 1 meter minus 1 meter
>does definitely not equal 0 meter before rounding off because any
>measurement is uncertain to some extent.
>
>Eckard Blumschein
Another collaborator for you might be Donald Shead, if you can overcome
your apparent fondness for the metric system.
Lee Rudolph
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