3 Jan
2000
3 Jan
'00
6:12 a.m.
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