Virgil
Posts:
4,482
Registered:
1/6/11
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 6, 2013 5:59 PM
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In article
<7a163160-c36a-46d0-ab7a-97cf0fa11578@q16g2000pbt.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> On Jan 6, 11:55 am, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <1038fe29-f169-4511-bd13-c7ade7fd1...@pd8g2000pbc.googlegroups.com>,
> > "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.
--
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