
Re: Simple analytical properties of n/d
Posted:
Mar 3, 2013 10:22 PM


On Sun, 3 Mar 2013, Ross A. Finlayson wrote:
> 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)?
> Answer: it is.
Only if n is a real variable.

