Re: .999... ?= 1

From: Virgil (ITSnetNOTcom/virgil_at_COMCAST.com)
Date: 06/09/04 

Date: Wed, 09 Jun 2004 12:57:52 -0600

In article <40C71A97.6030200@et.uni-magdeburg.de>,
 Eckard Blumschein <blumschein@et.uni-magdeburg.de> wrote:

> >>Who defined zero a number while excluding infinity from this status
> >>and why?
>
> Johan Kullstam wrote:
> > Because while you can add oo to the set of finite reals topologically,
> > it doesn't work as nicely as you would like algebraicly. In a
> > "field",
>
> For my understanding as a layman, no field is large enough as to include
> 00 while also no matrix is large enough as to represent a field with
> zero distance between its elements. In order to use 0 or 00 within a
> field, one has to abandon the meaning of distance from origin.

If "00" is Eckwhatever's symbol for infinity, "oo" would be less
ambigious, since two zeros, whether added, multiplied or juxtaposed
still looks like zero.

I am not aware of any field with zero distance berween its elements.
Could Eckwhatever please point one out.
>
> we can add, subtract, multiply and divide (by anything
> > non-zero). When you put oo (and perhaps -oo) into the mix, you lose
> > nice properties like being able to cancel
>
> Infinitely large means.

???

> There is no larger number. Putting such thing
> into any fixed framework is pure nonsense.
>
> > Sometimes people do work with the "extended reals" (the real numbers
> > with +oo and -oo).
>
> Why not?
>
> This is a compact space.
>
> Who claims that?
>
> > I've seen it used in point-set topology and in Lebesgue theory of
> > integration.
> >
> > You can add an infinite number of infinite quantities if you like.
> > Look at Abraham Robinson's non-standard analysis.

Why don't you try looking at it before pontificating on it.

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