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

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Cantor's first proof in DETAILS
Posted: Dec 5, 2012 11:06 PM

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.

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.)

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.

Simply it accumulates, the value: empty: full. How many grains of
sand is a dune? All of them.

And that would be infinitely out through the integers, because it is
somewhere, and not for any finite is it. That's the way it is: via
reason.

Work.

Zero: a real quantity.

Regards,

Ross Finlayson

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
12/4/12 ross.finlayson@gmail.com
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
12/7/12 Virgil
12/8/12 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 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
12/10/12
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