Re: MATH: Surreal numbers?

Geoff Smith (
Mon, 10 Nov 1997 16:41:50 -0800 (PST)

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.

I think I'll find the article and read it again.