Date: Jan 23, 2013 11:51 AM Author: David Bernier Subject: Re: ZFC and God On 01/23/2013 08:36 AM, Jesse F. Hughes wrote:

> WM<mueckenh@rz.fh-augsburg.de> writes:

>

>> On 23 Jan., 12:47, "Jesse F. Hughes"<je...@phiwumbda.org> wrote:

>>> WM<mueck...@rz.fh-augsburg.de> writes:

>>>> On 22 Jan., 21:18, "Jesse F. Hughes"<je...@phiwumbda.org> wrote:

>>>>> WM<mueck...@rz.fh-augsburg.de> writes:

>>>

>>>>>> That is potential infinity. That proof is not necessary, because the

>>>>>> set is obviously potentially infinite. No, you shoudl give a proof,

>>>>>> that there is a larger k than all finite k.

>>>

>>>>> Er, no. When I say that the union is infinite, I do not mean that it

>>>>> contains an infinite number.

>>>

>>>> But you mean that the tree contains infinite paths. And just that is

>>>> impossible without ...

>>>

>>>> In order to shorten this discussion please have a look at

>>>

>>> http://math.stackexchange.com/questions/284328/how-to-distinguish-bet...

>>>

>>> No. It's irrelevant.

>>

>> You are in error.

>>>

>>> We're talking about whether you can prove that

>>>

>>> U_n=1^oo {1,...,n}

>>>

>>> is finite. I'm not switching topics to paths in trees (despite the

>>> fact that the ignorance of your question is obvious).

>>

>> The union of FISs is finite. Yes that is my claim. But I cannot give

>> an upper limit, because the finite numbers have no upper limit. This

>> is called potentially infinite.

>>>

>>>> There it has meanwhile turned out ... But see it with your own eyes

>>>> what you would not believe if I told you.

>>>

>>>> The index omega is in reach, it seems.

>>>

>>> You're playing your usual little game of trying to change the topic.

>>> I won't have it.

>>>

>>> I take it that this new tack is so that you don't have to concede the

>>> point: there is no mathematical publication which claims that the

>>> above union contains elements larger than any natural, nor any

>>> publication which claims that this is what it means to be infinite.

>>

>> I know. But if you hace read the discussion, you have seen that two

>> matheologians claim just this. Why do they? Because they cannot answer

>> the question: What paths are (as subsets of the set of nodes) in a

>> Binary Tree that is the union of all its levels? Are there only the

>> finite paths? Or are there also the infinite paths?

>> Try to answer it, and you will see that you need the omegath level or

>> must confess that it is impossible to distinguish both cases. Hence,

>> Cantor's argument applies simultaneously to both or to none.

>

> I'm not interested in the web-published claims of two individuals on a

> different topic than we're discussing.

>

> Once again, let me remind you what you claimed. You claimed ZF was

> inconsistent, and in particular that ZF proves that the union

>

> U_n {1,...,n}

>

> is both finite and infinite.

>

> Now, we've had two competing definitions of infinite in this

> particular discussion.

>

> (1) A set S is infinite if there is no natural n such that |S| = n.

>

> (2) A set S is infinite if it contains a number greater than every

> natural n.

>

> The first definition is what mathematicians almost always mean, and

> they *never* mean the second, but this is mere semantics. Let's talk

> results.

>

> We both agree that, using definition (1), the above union is infinite

> and (I think) we agree that we cannot show it is finite (=not

> infinite). If I'm mistaken on this point, then please show me.

>

> On the other hand we both agree that, per definition (2), the union is

> "finite", but I have seen no contradiction result, since you have not

> shown that the union is "infinite" in this sense. Nor can you find a

> single publication in which a mathematician has claimed the union

> above (i.e., the set N of natural numbers) contains an element larger

> than every natural.

>

> So, let's not get distracted by paths and whatsits. Just do what you

> said you could do: show that ZF proves a contradiction. Either show

> me that there is a natural k such that

>

> | U_n {1,...,n} | = k

>

> or show me that there is an element k in U_n {1,...,n} such that k is

> larger than every natural number.

>

> But don't distract us from the topic at hand.

>

I love logical "theological" debate from you. Anyway, it's no use

ex-communicating WM, right? Better face the "heretics" head-on

with logic!

David Bernier

--

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Please specify a *single* volume group to restore.