Re: Have you ever wondered.....
From: AllYou! (idaman_at_conversent.net)
Date: 12/22/04
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Date: Wed, 22 Dec 2004 15:00:17 -0500
"Kees Roos" <croos@xs4all.nl> wrote in message
news:41c9c145$0$149$e4fe514c@news.xs4all.nl...
> "AllYou!" <idaman@conversent.net> schreef in bericht
> news:9MGdnY0LNYKRGlXcRVn-1g@conversent.net...
> Anyway, since it is clear that you don't have a clue of calculus
> and don't want to learn anything on the subject this will
> get us nowhere.
>From your own link:
"Consider a cross-section of the sphere as shown. This cross-section is a circle with
radius f(x) and area p[f(x)]2. Informally speaking, if we "slice" the sphere vertically
into discs, each disc having infinitesimal thickness dx, the volume of each disc is
approximately p[f(x)]2 dx. If we "add up" the volumes of the discs, we will get the volume
of the sphere:"
The key words there are *Informally speaking*, *infinitesimal thickness* (which means a
variable continuously approaching zero as a limit, but it never actually gets there), and
*approximately*. IOW, your own link fails to make your point. In fact, it makes mine.
As to calculus, this from the site:
http://tutorial.math.lamar.edu/AllBrowsers/2413/TypesOfInfinity.asp
"Most students have run across infinity at some point in time prior to a calculus class.
However, when they have dealt with it, it was just a symbol used to represent a really,
really large positive or really, really large negative number and that was the extent of
it. Once they get into a calculus class students are asked to do some basic algebra with
infinity and this is where they get into trouble. Infinity is NOT a number and for the
most part doesn't behave like a number. However, despite that we'll think of infinity in
this section as a really, really, really large number that is so large there isn't another
number larger than it. This is not correct of course, but may help with the discussion in
this section."
Clearly, infinity is *not a number* and therefore division by infinity yields nothing
useful, and certainly not zero. All other sites I've visited speak in the abstract of
dividing a number by infinity to yeild something. However, this is never done for more
than abstract purposes and never results in zero except in computer programs. The real
test of the applicability of this process is to take zero and multiply it by infinity.
What number will you get then?
Find me one site which shows that multiplication of zero by infinity yields any real
value.
Your basic misunderstanding of calculus is that you don't know the difference between a
function which has zero as a limiting value and the value of zero itself. Don't berate me
on an issue unless you're sure you know what you're talking about in the first place.
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