Re: Galileo's Paradox

Eckard Blumschein wrote:
On 12/7/2006 1:30 AM, David Marcus wrote:
Eckard Blumschein wrote:
On 12/6/2006 5:35 AM, David Marcus wrote:
Eckard Blumschein wrote:

You did not understand that I am using Fourier transform as an example.

Example of what?

a typical mistake when using the immediate value.

Be specific: what is the mistake?

Ask Hendrik van Hees who could not explain a result differing from a
printed one just by the factor 2. He uttered this in sci.physics.research

Don't be silly (or sillier than you usually are). Either you know of a
mistake or you don't. If you can't tell us the mistake, then stop saying
there is one. The fact that someone else is having problems with math
isn't relevant. Lots of people have trouble with math. That doesn't mean
there is something wrong with mathematics.

I do not criticize FT but the integral tables, and I did not have a
problem myself but I recall several reported cases of unexplained error
by just the trifle of two. The integral tables suggest using the
intermediate value.

You are criticizing integral tables?

Some of them are rather eclectic and difficult to overlook. Others are a
bit slim. Sometimes the intermediate values are given, sometimes they
are omitted which i consider the better decision.

I haven't a clue why you think integral tables have any relevance to set
theory.

The intermediate values, given in integral tables "for mathematical
reasons", are misleading and perhaps unnecessary.

No idea what "mathematical reasons" these are. Please give a full quote
where the book says what the "mathematical reasons" are.

The "mathematical
reasons" relate to the somewhat inappropriate arbitrarily distorted
notion of real numbers adapted to the illusion by Dedekind and Cantor,
real numbers and infinity are numbers with full civil rights.

You really should learn to speak concretely. Telling us what they
"relate to" tells us nothing, especially since the rest of your sentence
just contains your usual prejudiced, uninformed rant.

Experienced mathematicians should indeed know that
they must avoid this use. Some tables give the intermedite value for the
sake of putative mathematical correctness.

Please give an example.

A gave
http://iesl.et.uni-magdeburg.de/~blumsche/M283.html

That link produces a page saying the search didn't produce any results.
Kind of ironic since all of your postings contain no results, too.

I just have my old Bronstein-Semendjajew Teubner 1962 at hand.
On p. 351, number 13 does not give intermediate values, number 15 does.

Please quote the entire example. Not everyone is next to a library.

No. 15: Integral from 0 to oo dx over sin x cos x / x =
= pi/2 for |a|<1
= pi/4 for |a|=1 (intermediate value)
= 0 for |a|>1

There is no "a" in int_0^oo sin x cos x / x.

No. 13: just over tan(ax)/x

Huh?

Others omit it.
As long as one knows the result in advance, there is almost not risk. FT
and subsequent IFT may perform an ideal check of set theory.

What do you mean "ideal check of set theory"?

Set theory leads to intermediate values.

What do you mean? Do try to be specific.

Set theory considers real numbers to be existing numbers, not just
fictions.

Nonsense. The words "existing" and "fictions" are your own creation. Set
theory says nothing of the sort. If you discuss something, you should
have at least some knowledge of it.

From this point of view, one cannot admit that a number may be
void even if it turns out to be useless and maybe even misleading.

More made-up words: "void", "useless", "misleading".

--
David Marcus
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... most of the standard axioms would get scrapped ... you claim that set theory is ... theory in which to express virtually all of mathematics. ... S (call this function 'omega pre S'). ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... What I mean is set theory was not born just by the great thought of Cantor. ... of mathematics behind, which help greatly, and which even where necessary for the theory to be imagined. ... formalization, at a level up, for meta-theory. ... scientists and engineers doesn't have to be used by engineers. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... What I mean is set theory was not ... >> prove only the mathematics we set out to prove and not statements about ... >> formalization that does not compromise the other criteria. ... >> or show a formalization that does not compromise the other criteria. ...
    (sci.math)
  • Re: Das Kalenderblatt 090921
    ... as the appropriate foundation for modern mathematics, ... and set theory itself, ... Unter einer „Menge“ verstehen wir jede Zusammenfassung M von ... Die Existenz von R baut sich auf die " Dedekind'schen Schnitte " auf - ...
    (de.sci.mathematik)
  • Re: Kuratowski Ordered Pair
    ... notions of temporality and things like that, ... operation and mathematics seems to do just fine with the Kuratowski ... definitions are offered by detractors of the Kuratowski definition? ... Fromout set theory ...
    (sci.math)
Quantcast