
Re: ran(EF) contains ~EF(n)
Posted:
May 1, 2013 12:22 AM


On Tue, 30 Apr 2013, Ross A. Finlayson wrote: > On Apr 30, 8:34 pm, William Elliot <ma...@panix.com> wrote:
> "EF_d(n) is n/d for 0 <= n/d <= 1 for natural integers n, d, as d goes > to infinity." > EF, or f for short, isn't a function, it's a group of functions f_d with the property, f_d(n) = n/d provided n <= d. Thus to make some sense of you hand waving:
For d in N, f_d is a function from { 1,2,.. d } into [0,1] that maps n to n/d.
How are you defining f = lim(d>oo) f_d. Pointwise? Then f(n) = lim(d>oo) n/d = 0, except that f_d isn't defined for all n in N.
So you'e defining f_d to be over N mapping n to min{ n/d, 1 }. Thus f(n) = lim(doo) min{ n/d, 1} = 0 for all n in N.

