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Topic: The Distinguishability argument of the Reals.
Replies: 83   Last Post: Jan 7, 2013 12:58 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: The Distinguishability argument of the Reals.
Posted: Jan 6, 2013 1:10 AM

In article
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:

> On Jan 5, 7:37 pm, fom <fomJ...@nyms.net> wrote:
> > 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.

>
>
> lim_n->d n/d = 1

Since the set of values of n is finite for each value of d, no limit
process is required, or even defined.

One has f(d,d) = 1 for all d, but one does not have f(n,d) = 1 for any
n less than d, and one has the properly defined limit:

lim_(d -> oo) f(n,d) = 0 for every n in N
--

Date Subject Author
1/1/13 Zaljohar@gmail.com
1/2/13 mueckenh@rz.fh-augsburg.de
1/2/13 Virgil
1/3/13 Virgil
1/3/13 Zaljohar@gmail.com
1/3/13 gus gassmann
1/3/13 Zaljohar@gmail.com
1/3/13 gus gassmann
1/3/13 Zaljohar@gmail.com
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 fom
1/4/13 Zaljohar@gmail.com
1/4/13 fom
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 fom
1/3/13 Virgil
1/4/13 gus gassmann
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/4/13 Virgil
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/4/13 Virgil
1/4/13 gus gassmann
1/4/13 ross.finlayson@gmail.com
1/5/13 Virgil
1/5/13 ross.finlayson@gmail.com
1/5/13 Virgil
1/5/13 fom
1/5/13 ross.finlayson@gmail.com
1/6/13 fom
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/6/13 ross.finlayson@gmail.com
1/6/13 Virgil
1/7/13 ross.finlayson@gmail.com
1/7/13 Virgil
1/3/13 fom
1/3/13 fom
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/6/13 Virgil
1/6/13 fom
1/6/13 Virgil
1/6/13 fom
1/6/13 ross.finlayson@gmail.com
1/4/13 Virgil
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/3/13 forbisgaryg@gmail.com
1/3/13 Virgil
1/4/13 Zaljohar@gmail.com
1/4/13 Virgil
1/4/13 Zaljohar@gmail.com
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 fom
1/5/13 mueckenh@rz.fh-augsburg.de
1/5/13 Virgil
1/5/13 fom
1/5/13 Virgil
1/4/13 Virgil
1/3/13 mueckenh@rz.fh-augsburg.de
1/3/13 Virgil
1/4/13 mueckenh@rz.fh-augsburg.de
1/4/13 fom
1/4/13 Virgil
1/2/13 Bill Taylor