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Topic: Cantor's first proof in DETAILS
Replies: 85   Last Post: Dec 10, 2012 7:23 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Cantor's first proof in DETAILS
Posted: Dec 5, 2012 11:53 PM

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

> On Dec 4, 1:22 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
> >

> > > And, m > n implies EF(m) > EF(n), because here m > n.  It is true,
> > > that.  The functions there modeling it are all constant monotone
> > > increasing, and they all go to one.

> >
> > IN your origin definitions, you had  EF_n(m) = 1/n, for 1 <= m <= n,
> > so that SUM_(x=1..n) EF_n(x) = 1, for all n and then defined you EF()
> > also the limit function of the EF_n() as n -> oo.
> >
> > That did not work then and does not work now.
> > --

>
>
> EF_d(n) = n/d, and EF = EF_oo.

From which EF_d(n) < EF_d(n+1) whenever n < d < oo.

So for which n in |N, if any, is Ef(n) < EF(n+1)?

EF_n(n) = 1 for all n in |N, so is EF_oo(oo) = 1 ?

Ross has left too many unanswered questions about the nature of his
alleged EF for it to be anything useful.
>
>
> It does work: n+1 > n => (n+1)/m > n/m, for non-negative m, n. There
> is a constant monotonic difference between each EF(n) and EF(n+1), for
> example where zero is less than one, in trichotomy of the integers.
> Standardly in the limit EF(0) = 0 and lim_n->d EF(n) = 1. The
> constant monotonic differences sum to one. (The limit is the sum.)

Which limit is which sum? A if anyone cares.
>
> And yes, we're all aware that lim_d->oo n/d = 0, and also that n+1 > n
> => (n+1)/d > n/d, for all positive n, d (d strictly). Then, It is
> simply via symmetry, that the range of EF is [0,1] and the range of
> the complementary or reverse EF is [1,0], that they cross at 1/2,
> their average, constant over all values.

If you could only make your nonsense funny, it might be worth something,
but as it is, dull as dishwater and corrupted by internal
--

Date Subject Author
11/25/12 ross.finlayson@gmail.com
11/25/12 Virgil
11/25/12 ross.finlayson@gmail.com
11/25/12 Graham Cooper
11/25/12 ross.finlayson@gmail.com
11/25/12 Virgil
11/25/12 ross.finlayson@gmail.com
11/26/12 Virgil
11/26/12 ross.finlayson@gmail.com
11/26/12 Virgil
11/26/12 ross.finlayson@gmail.com
11/26/12 Virgil
11/27/12 ross.finlayson@gmail.com
11/27/12 Virgil
11/27/12 ross.finlayson@gmail.com
11/27/12 Virgil
11/27/12 ross.finlayson@gmail.com
11/28/12 Virgil
11/28/12 ross.finlayson@gmail.com
11/28/12 Virgil
11/28/12 ross.finlayson@gmail.com
11/28/12 Virgil
11/29/12 ross.finlayson@gmail.com
11/29/12 Virgil
11/29/12 ross.finlayson@gmail.com
11/30/12 Virgil
11/30/12 FredJeffries@gmail.com
11/30/12 ross.finlayson@gmail.com
11/30/12 FredJeffries@gmail.com
11/30/12 ross.finlayson@gmail.com
12/1/12 Virgil
11/30/12 ross.finlayson@gmail.com
12/1/12 Virgil
12/1/12 ross.finlayson@gmail.com
12/1/12 Virgil
12/1/12 FredJeffries@gmail.com
12/1/12 ross.finlayson@gmail.com
12/1/12 Virgil
12/2/12 ross.finlayson@gmail.com
12/2/12 Virgil
12/2/12 ross.finlayson@gmail.com
12/2/12 Virgil
12/3/12 ross.finlayson@gmail.com
12/3/12 Virgil
12/3/12 Virgil
12/3/12 ross.finlayson@gmail.com
12/3/12 Virgil
12/3/12 ross.finlayson@gmail.com
12/4/12 Virgil
12/4/12 ross.finlayson@gmail.com
12/4/12 Virgil
12/4/12 ross.finlayson@gmail.com
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12/4/12 Virgil
12/4/12 Virgil
12/4/12 Virgil
12/5/12 ross.finlayson@gmail.com
12/6/12 Virgil
12/7/12 ross.finlayson@gmail.com
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12/8/12 ross.finlayson@gmail.com
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12/9/12 ross.finlayson@gmail.com
12/9/12 Virgil
12/9/12 ross.finlayson@gmail.com
12/9/12 ross.finlayson@gmail.com
12/9/12 Virgil
12/9/12 ross.finlayson@gmail.com
12/9/12 Virgil
12/9/12 ross.finlayson@gmail.com
12/9/12 Virgil
12/9/12 ross.finlayson@gmail.com
12/10/12 Virgil
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12/4/12 Virgil
12/5/12 ross.finlayson@gmail.com
12/5/12 Virgil
11/30/12 Virgil
11/25/12 Graham Cooper
11/25/12 Virgil
11/25/12 ross.finlayson@gmail.com
11/25/12 Virgil