Virgil
Posts:
4,482
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 5, 2013 10:06 PM
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In article
<bc8606cb-65f9-487f-854c-ac576d414455@l3g2000pbq.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> On Jan 4, 10:20 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <7850ae29-08d9-49ef-8c7b-e8979e037...@m4g2000pbd.googlegroups.com>,
> > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
> >
> > > Consider the function that is the limit of functions f(n,d) = n/d, n =
> > > 0, ..., d; n, d E N.
> >
> > You mean the zero function?
> >
> > For every n, the limit of f(n,d) as d -> oo is 0, so your limit function
> > would have to be the zero function: f(n,oo) = 0 for all n.
> > --
>
>
> No, none of those is the zero function, and each d->oo has it so that
> d/d = 1. but for any fixed n, n/d -> 0 as d -> oo.
But for every n in {0,1,2,..., d}, Lim_(d-> oo) n/d = 0
So that if your f(n,d) is a function of d for fixed n, as you indicate,
Lim_(d-> oo) n/d = 0
>
> Here the range of the elements are defined by their constant monotone
> difference, the sum of which, is one.
For any fixed d, the range of n is from 0 to d.
For any fixed n, the range of d is from n upwards.
At least as you have defined your alleged function.
Another of Ross' fakes!
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