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Re: Paul Lutus says dumb things
Posted:
Dec 2, 2001 1:31 PM
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"David W. Cantrell" <DWCantrell@sigmaxi.org> wrote in message
news://20011202102151.262$Tr@newsreader.com...
> > I chose to express it as "as x approaches 0, 1/x approaches infinity."
>
> Chose (past tense)? If you had expressed it that way before, I would
> never have said "badly butchered". Your new statement makes good sense.
Again, thanks for your support, no irony intended. Many in this and a prior
thread have argued that a limit statement literally assigns the limit value
to the relevant variable, in other words, that a numeric variable x equals
infinity.
My previous post included the form I was arguing against, not the one I was
supporting. The clue is my use of "which, of course, is false ..." Here is
the original:
> > > "as x approaches the limit of zero, 1/x equals infinity"
> > >
> > > -- which, of course, is false and is not what a limit represents.
> > In either way of saying it, this is a special use of the equals sign,
> > with something other than the naive interpretation. My original point.
>
> But that original point is wrong. There is no "special use of the equals
> sign" in evidence. Limit_{x->0} 1/x = infinity is true in the projective
> extension, with "=" being used in the normal way.
But it doesn't mean that x equals infinity. That is a limit, not an
assignment. I know you may find this surprising, but that was the issue --
several people began arguing that x equaled infinity, and that therefore
infinity is a number in a default number system, one for which arithmetic
operations are defined in a conventional way.
It is like saying, "On Wednesday, we are in Cleveland." This does not say,
"We are in Cleveland." Same idea, and others have argued that the second
phrase summarizes the intention -- that x equals infinity, period.
A quick reading of the thread shows this clearly.
The debate quickly wandered off to the issue of extended reals, a separate
topic, one hardly bearing on whether the original assertion is correct or
meaningful, in a number system in which arithmetic operations are defined in
a conventional way.
--
Paul Lutus
www.arachnoid.com
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