categories: Re: Real interval halving

[Michael Barr <barr@barrs.org>]

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.  Anyway, Let S be the ring of
functions s: N --> N such that the function of two variables (m,n) |-->
s(m+n) - s(m) - s(n) is bounded.  Addition is element-wise and
multiplication is functional composition.  Let I consist of the bounded
sequences.  Then R = S/I.  Interestingly, S is not commutative.

We now have a real tangent line.

Michael