> Survey: does anybody find that: > lim_d->oo lim_n->d n/d = 1 > > It's clear that it does, for all values of d e N. > > Then, as a function f = n/d from N to R[0,1], d e N, n <= d E N, is it > not constant monotone increasing?
Is that f(d) = n/d or f(n) = n/d? What's deN and dEN?
> If not increasing, how is lim_n->d n/d = 1?
lim(x->d) x/d = 1, because since f(x) = x/d is continuous, lim(x->d) x/d = d/d = 1
For integer variables n, lim(n->d) f(n) is meaningless. Give a definition for it. Wouldn't it be the same as f(d)?