Date: Jan 5, 2013 10:37 PM
Subject: Re: The Distinguishability argument of the Reals.
On 1/5/2013 6:35 PM, Ross A. Finlayson wrote:
> On Jan 4, 10:20 pm, Virgil <vir...@ligriv.com> wrote:
>> In article
>> "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.
That is true.
The problem is that as d -> oo the value at any
given fixed n -> 0.
2/3, 2/4, 2/5, 2/6, 2/7, 2/8, 2/9, 2/10, ...
So, the pointwise limit of the function is zero.