# Re: MATH: Surreal numbers?

Michael Lorrey (retroman@together.net)
Wed, 12 Nov 1997 09:34:36 -0500

Geoff Smith wrote:
>
> On Mon, 10 Nov 1997, byteboy wrote:
>
> > This might have already been covered in the infinities thread, it seems
> > I came into this mailing list a bit late. If this tidbit has already
> > been covered, please accept my apologies and ignore this message.
> >
> > Awhile back I read an article in some magazine that I can't remember -
> > maybe it was a MENSA thing (eep, the M-word!), maybe Popular Science, I
> > don't know - but it was on this new concept called Surreal Numbers.
>
> Discover Magazine. "Surreal Numbers." Forget which issue.
>
> > Now, at the time, I was just learning about _imaginary_ numbers, so
> > the thought that numbers could be surreal was something I liked to think
> > about from time to time, but never got into - no one could teach me but
> > myself. Anyway, it seems that some mathematics theorist was coming up
> > with all these crazy notions about numbers such as infinity + 1, and was
> > calling them surreal numbers. Has anyone else heard of such a thing or
> > is my memory playing tricks on me?
>
> Yep. Surreal numbers are denoted by up and down arrows. An up arrow with
> a dot on top means go up omega times (omega being the set of all integers)
> Surreal numbers are used to distinguish from different types of
> infinities. For example, the number of integers is obviously different
> than the number of real numbers, yet we call them both infinity.
>

Yeah, the idea that the number of numbers between 0 and 1 was equal to
the total number of numbers was a bit incomprehenible to me back in
school. Glad to see that there is at least SOME differentiation.

```--
TANSTAAFL!!!
Michael Lorrey
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