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Re: Paul Lutus says dumb things
Posted:
Dec 3, 2001 9:48 AM
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On Sun, 02 Dec 2001 22:30:06 GMT, "Paul Lutus"
<nospam@nosite.zzz> wrote:
> "Angus Rodgers" <angus_prune@bigfoot.com> wrote in message
> news://2d6l0u81dedl6pmhinikob8ck33pmv7ci3@4ax.com...
>
> > You haven't realised it yet, but you have been making a fool of
> > yourself in sci.math by talking very condescendingly and abruptly
> > to several mathematicians who really do know their stuff.
>
> Example? Surely you don't think mathematicians cannot err in a
> conversation composed mostly of words, do you?
Well, OK. I don't think I'm going to get far by doing this, so I'm
not going to persist for long; and I can't face reading through all
these threads again, to find the most compelling example; but here,
I think, is the *first* time you did it:
On Fri, 30 Nov 2001 00:31:10 GMT, "Paul Lutus"
<nospam@nosite.zzz> wrote:
> "Mike Oliver" <oliver@math.ucla.edu> wrote in message
> news://3C06C01D.15E3D8C1@math.ucla.edu...
> > Paul Lutus wrote:
> >
> > > What? Infinity is not a number. Therefore 1/Infinity is also
> > > not a number.
> >
> > Eh? How does that follow?
> >
> > If Infinity is something other than a number, then if you want
> > to divide 1 by it, you'll have to extend the division operation
> > to whatever kind of object Infinity is. How do you know, a
> > priori, that you won't sometimes get numbers as output from the
> > extended operation?
>
> Because infinity is not a number. Therefore any effort to include
> it in a numerical operation ipso facto produces a meaningless result.
>
> Did you brush up on your math knowledge yet?
Notice how you (1) merely reiterated your assertion, instead of
rebutting its rebuttal, and (2) threw in a gratuitous insult to
someone more knowledgeable than yourself about the matter under
discussion.
See what I mean? (Let me guess: no.)
> Perhaps you refer to the post by Chan-Ho Suh in which this
> appeared:
> > [...]
I don't know, because you haven't quoted any insulting remarks
in that context.
(Anyway, I wasn't referring to just one article.)
> In a later post, I used a complementary, more relevant example
> in which 1/x approaches infinity. Then the sparks began to fly.
> Clearly this --
>
> lim x->0, 1/x = infinity
>
> -- means "as x approaches zero, 1/x approaches infinity."
[Two corrections incorporated here.]
> Or one might say "1/x equals infinity in the limit," a way of
> saying it that is more likely to produce confusion among non-
> specialists on first reading.
[Another correction incorporated.]
I think we can all agree on that.
But you should be aware (by now!) that it is possible in some
circumstances to define an entity oo such that the expression
"lim (x -> 0) 1/x" has the value oo in exactly the same sense
as the expression "lim (x -> 1) 1/x" has the value 1.
The key is to define "neighbourhoods" of oo which share those
abstract properties already possessed by the "neighbourhoods"
of real numbers, such as 1, that allow the concept of a limit
to be defined. This kind of generalisation by abstraction is
quite common in mathematics, even in the construction of the
real numbers themselves. (I won't bore you with the details,
unless you're interested. Also, I'm rusty, and will probably
get everything wrong! Best to leave it to others, methinks.)
> > But you're not the first person to do this; indeed, it is
> > something of a tradition here. Also, you may be partly
> > excused, if indeed it does turn out that there is something
> > of a sci.physics vs. sci.math culture clash involved.
>
> No doubt to the delight of the cowardly, anonymous troll who
> initiated the present thread, and who has since tried unsucc-
> essfully to insert alt.flames in the cross-post list.
Oh, there's some trolling going on, all right. (No, I don't
mean just by you!)
--
Angus Rodgers (angus_prune@ eats spam; reply to angusr@)
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