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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 6:32 PM

On Tuesday, August 12, 2014 12:52:24 PM UTC-7, muec...@rz.fh-augsburg.de wrote:
> On Tuesday, 12 August 2014 20:06:10 UTC+2, Zeit Geist wrote:
> > On Tuesday, August 12, 2014 9:43:11 AM UTC-7, muec...@rz.fh-augsburg.de wrote:
> > > On Tuesday, 12 August 2014 18:56:23 UTC+2, Ralf Bader wrote:

> > > > > We all agree that a bijection up to every FIS is possible.

> > > > No, we do not agree. The phrase "bijection up to every FIS" is without any
> > > > sense.

> > > The alternative is a bijection including the last element.

> > Since we have Infinite Sets, we Can Construct Infinite Functions. This includes Bijections.

> Only for every finite initial segment.

Why's that?

By the Definition of "Bijection", since for there Not to Exist a Bijection between N and Q, We would need to Find, for any Function, F: N -> q, some Q_E such that q_e had No Pre-Image in N.
(This is True, because we Already Know that there is some 1:1 Function from N to Q, the Function I(n) = n.). Now, we have an Algorithm that Defines a Function E, which can be Written in a Finite Number of Symbols, from which can Find the n e N, such that E(n) = q. And if p is one of the Infinitely Many Rationals that Follow q in the Enumeration, then we can Prove the Existence of some m such that E(m) = p.

This Actually Proves that For Every Initial Segment, your Requirement is Fulfilled.
And also, if your Requirement is Fulfilled, then We have a Bijection.

> > No, Last Elements are Necessary.

> That was not the question. Fact is: no last element is present in the bijection. What remains is FIS.
>

But, We have an Algorithm with tells us For Any n e N which q e Q is the Image of n.
And, vice versa, For Any q e Q which n e N is the Pre-Image of q.
Why do you Insist that we Need a Last Element in order to have a Bijection?

> > Now, if you have a Proof an Infinite Set can Not Exist, in ZF \ { The Axiom of Infinity }, then Present it. BTW, your "Proof" that N can Not Exhaust Q is Invalid. It Contains a Non-Sequitur. You have been Shown where.

> I have been informed by a fool that his opinion differs from mine.

No Opinion. Logical Facts, actually.
Why don't You Write down the Definitions of "Bijection" and "Potential Infinity" and someone can Show how these Definitions are Inconsistent or just simply Lead to the Usual Definitions.

> I consider this irrelevant.

So what?
That's what you do when your Misunderstandings of Logic back you into a Logical Corner.

> Regards, WM

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 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 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