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Topic: Is zero an approximation?
Replies: 170   Last Post: Dec 8, 2001 12:57 AM

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 Mike Oliver Posts: 1,518 Registered: 12/6/04
Re: Is zero an approximation?
Posted: Nov 30, 2001 4:14 AM

Paul Lutus wrote:
> "Mike Oliver" <oliver@math.ucla.edu> wrote in message
> news://3C07175E.6985DD03@math.ucla.edu...

> > Lutus, you're being an ass. Solipsism doesn't enter into it.
>
> It didn't until you drifted into it. Then it became the issue. You have
> chosen to ignore any commonly accepted definitions appropriate to the
> original context. That is how solipsism is defined.

Find me these "commonly accepted definitions" in some respectable source.
Show me in Bourbaki where it says a "number system" has to satisfy additive
cancellation. Show me in Lang, show me in Hungerford, show me in Folland,
in Rudin, in *any* decent graduate-level algebra or analysis text. You
can't, because no one writing at that level would say such a silly thing.

> And, regardless of the multitude of special-case definitions, consider the
>

> > Is zero an approximation?
> > An approximation of zero, where zero is actually 1/infinity?

>
> For someone who posts an inquiry like this, my reply is the appropriate one.
> Zero is not "actually 1/infinity."

Well, in the extended complex numbers, it actually is. And it is very
possible that the extended complex numbers are the natural structure to
capture the intuitions he was trying to get at, even if he expressed them
poorly.

They *are* an extremely natural structure, you know. You just take C,
one-point-compactify it, and then extend the basic operations to the
maximum domains they can have subject to continuity. This can be done
in a unique manner, and it's both a natural and a useful thing to do.

Their algebraic properties are not super-mega-friendly. Tough titties.
It's a luxury to be able to specify the algebraic properties you want
your structure to have. Lots of times, the structure you want to consider
is fixed, and its algebraic properties are what they are.

Date Subject Author
11/29/01 Jim Bob
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11/29/01 Mike Oliver
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