Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 8:19 PM

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

> On Jan 6, 2:59 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
> >
> >
> >
> >
> >
> >
> >
> >
> >

> > > On Jan 6, 11:55 am, Virgil <vir...@ligriv.com> wrote:
> > > > In article
> > > >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

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

> >
> > > > > No
> >
> > > > If, as Ross defined it, f(n,d) = n/d for all d in N and all n in
> > > > {0,1,2,...,d}, then for any n, lim_(d -> oo) f(n,d) = 0

> >
> > > > And no amount of denial by Ross will alter that fact.
> > > > --

> >
> > > Wait, aren't you going to misquote Einstein?  Because, you have quite
> > > the practice of misquoting me.  Now, I'm no Einstein, but, I generally
> > > heartily agree with him, of the rather conscientious sort.

> >
> > >    d/d = 1
> > >    lim_(n->d) n/d = 1
> > >    lim_(n->d, d->oo) n/d = 1

> >
> > That last one is false because
> >  lim_(n -> d) [ lim_(d -> oo) n/d ] =lim_(n -> oo) 0 = 0
> >  lim_(d -> oo) [ lim_(n -> d) n/d ] =lim_(n -> oo) 1 = 1
> > SO
> >  lim_(d->oo)(lim_(n->oo) n/d =/= lim_(n->oo)(lim_(d->oo) n/d
> >
> > SO Ross's lim_(n->d, d->oo) n/d does not exist!
> >
> > At least in stndard mathematics.
> >
> > But he might try in in WMytheology or RAFeology.
> > --

>
>
> http://en.wikipedia.org/wiki/Order_of_integration_(calculus)
>
> It's not quantifier dyslexia so much as that there's only one free
> parameter modeling the function: d.
>
> There d, for denominator, for n, numerator: is free and unbounded, as
> is n, as it ranges through elements simply enough in d. For all
> values of d, the range is [0,1].

For each value of d, the range is a finite subset of d+1 values in [0,1].
You may properly may say that the codomain for each d is [0,1], but the
range is the set of values values actual taken by the function, and for
each value of d the range is a set of d+1 values, not an interval.

Wrong again, Ross!
--

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