categories: Re: Schanuel's reals

[Ross Street <street@ics.mq.edu.au>]

Mike Barr writes:
>Perhaps Vaughan is unfamiliar with the following definition of the reals.
>I got it from Steve Schanuel.  I believe that he got it from Serge Lang
>and he probably got it from Emil Artin.

I believe the idea *came* from Artin but I don't believe Artin was 
thinking of it as a *construction* of the reals.  I was so taken by 
the construction that I thought it should be better known by tertiary 
teachers.  I wrote a little note

	An efficient construction of the real numbers,
	Gazette Australian Math. Soc. 12 (1985) 57-58

on the construction (giving credit to Schanuel and reporting that 
Peter Johnstone told me Richard Lewis from Sussex had also come up 
with it).
[Warning and Challenge: Steve pointed out that my note messes up the 
construction of the sup operation.]

Happy 2000 plus.

Ross