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Topic: § 534 Finis
Replies: 153   Last Post: Aug 22, 2014 11:58 AM

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 Tucsondrew@me.com Posts: 1,161 Registered: 5/24/13
Re: § 534 Finis
Posted: Aug 12, 2014 1:52 PM
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On Tuesday, August 12, 2014 8:37:19 AM UTC-7, FredJeffries wrote:
> On Tuesday, August 12, 2014 3:49:59 AM UTC-7, muec...@rz.fh-augsburg.de wrote:
>

> >
>
> > My proof contradicts at most the intuition of some matheologians who believe that a bijection observed up tp every n implies a complete bijection between infinity set.

> I am curious. Let's take a head count: who here "believe[s] that a bijection observed up tp [sic] every n implies a complete bijection between infinity set [sic]"?
>

Suppose that there Exists some Function, E: N -> Q; such that for Every n e N we have if E(n) = q and m < n, then E(m) ~= q. Obviously, this Excludes the Possibility that for ANY Pair of Naturals, say a and b, regardless of their Magnitude Relative to n, we have E(a) ~= E(b). This Shows E Must be 1:1.

Now, Showing that is Onto, is a little Trickier, for I'm Not sure what to Make of the Statement, "A SURJECTION observed up to Every n" Means. So, it will be Interpreted as, For Any q e Q, There Exists some n e N, such that for Some m <= n, we have E(m) = q. Which immediately Leads to There Exist some m e N such that E(m) = q. Thus E is Surjection, as well.

Hence E is, indeed, a Bijection, as Desired.

> You may answer for yourself (preferred) or say what you think some other person believes if you give evidence.

Here's a DISPROOF of the Above as Submitted by a Wandering Minstrel. He Claims to Refute the ONTO part of the Above Proof.

We Know that For Any n e N, if we Let G_n = { q e Q | There Exists an m <= n such that E(m) = q } then the Set Q \ G_n Contains an Infinite Amount of Unenumerated Rationals. Since that is True for ALL n, and N IS ALL n ( Nothing More! ) we MUST have that the Elements of N can Not Enumerate Every Element of Q. After all, if Every n Leaves an Infinite Amount of Rationals Unenumerated, what is Left to Enumerated the Remainder? This Shows that N can Not Ever Exhaust Q, and hence No Bijection Exists.

We can also see, that for All n e N, we have | G_n | = oo so Taking the Limit as n -> oo, we could Never have that the Codomain of E ( with Domain N ) is Finite, nonetheless Empty! Because Limits MUST be Continuous!

I'm Not sure which of the Above is Correct.
Perhaps, it Shows an Inconsistency in "Set Theory". Which "Set Theory"? I don't Know.

ZG

Date Subject Author
8/12/14 Tommy Jensen
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Virgil
8/12/14 FredJeffries@gmail.com
8/12/14 Martin Shobe
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Tanu R.
8/12/14 Tanu R.
8/12/14 Virgil
8/12/14 Tucsondrew@me.com
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Tanu R.
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Tanu R.
8/13/14 Virgil
8/12/14 Tanu R.
8/12/14 Virgil
8/12/14 Tucsondrew@me.com
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Virgil
8/12/14 Martin Shobe
8/12/14 Virgil
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Martin Shobe
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Martin Shobe
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Martin Shobe
8/13/14 Virgil
8/14/14 Martin Shobe
8/14/14 mueckenh@rz.fh-augsburg.de
8/14/14 Ralf Bader
8/14/14 Virgil
8/15/14 mueckenh@rz.fh-augsburg.de
8/15/14 Virgil
8/14/14 Virgil
8/14/14 YBM
8/15/14 Martin Shobe
8/15/14 mueckenh@rz.fh-augsburg.de
8/15/14 Virgil
8/15/14 Martin Shobe
8/15/14 Virgil
8/15/14 Martin Shobe
8/16/14 mueckenh@rz.fh-augsburg.de
8/16/14 Virgil
8/16/14 Martin Shobe
8/17/14 Virgil
8/17/14 mueckenh@rz.fh-augsburg.de
8/17/14 Martin Shobe
8/17/14 Martin Shobe
8/18/14 mueckenh@rz.fh-augsburg.de
8/18/14 Martin Shobe
8/19/14 mueckenh@rz.fh-augsburg.de
8/19/14 Martin Shobe
8/19/14 Virgil
8/19/14 mueckenh@rz.fh-augsburg.de
8/19/14 Virgil
8/19/14 mueckenh@rz.fh-augsburg.de
8/19/14 Virgil
8/19/14 Martin Shobe
8/20/14 mueckenh@rz.fh-augsburg.de
8/20/14 Virgil
8/21/14 Martin Shobe
8/21/14 mueckenh@rz.fh-augsburg.de
8/21/14 Tanu R.
8/21/14 Martin Shobe
8/21/14 mueckenh@rz.fh-augsburg.de
8/21/14 Martin Shobe
8/21/14 mueckenh@rz.fh-augsburg.de
8/21/14 Martin Shobe
8/21/14 mueckenh@rz.fh-augsburg.de
8/21/14 Tanu R.
8/21/14 Martin Shobe
8/22/14 Virgil
8/22/14 mueckenh@rz.fh-augsburg.de
8/22/14 Virgil
8/22/14 Virgil
8/21/14 Virgil
8/21/14 Virgil
8/21/14 mueckenh@rz.fh-augsburg.de
8/21/14 Virgil
8/21/14 Martin Shobe
8/21/14 mueckenh@rz.fh-augsburg.de
8/21/14 Tanu R.
8/21/14 Martin Shobe
8/21/14 Virgil
8/21/14 Virgil
8/19/14 Virgil
8/18/14 Virgil
8/18/14 Virgil
8/13/14 YBM
8/13/14 Virgil
8/13/14 Tanu R.
8/13/14 Virgil
8/13/14 Virgil
8/12/14 Martin Shobe
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Tanu R.
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Tanu R.
8/12/14 Virgil
8/12/14 Tucsondrew@me.com
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Virgil
8/12/14 Martin Shobe
8/12/14 Virgil
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Martin Shobe
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Martin Shobe
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Martin Shobe
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Virgil
8/14/14 Martin Shobe
8/14/14 mueckenh@rz.fh-augsburg.de
8/14/14 Virgil
8/15/14 Martin Shobe
8/15/14 mueckenh@rz.fh-augsburg.de
8/15/14 Martin Shobe
8/15/14 mueckenh@rz.fh-augsburg.de
8/15/14 Virgil
8/15/14 Martin Shobe
8/13/14 Virgil
8/13/14 Virgil
8/13/14 Virgil
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Virgil
8/12/14 Ralf Bader
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Virgil
8/12/14 Tucsondrew@me.com
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Virgil
8/12/14 Tucsondrew@me.com
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Virgil
8/12/14 Tucsondrew@me.com
8/12/14 Michael Klemm
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Virgil
8/12/14 Virgil
8/12/14 FredJeffries@gmail.com
8/12/14 Virgil
8/12/14 mueckenh@rz.fh-augsburg.de
8/12/14 Virgil
8/12/14 Tanu R.
8/12/14 Tucsondrew@me.com
8/13/14 mueckenh@rz.fh-augsburg.de
8/13/14 Virgil

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