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Topic: (infinity) A real story
Replies: 4   Last Post: Oct 12, 2013 6:08 PM

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Virgil

Posts: 6,964
Registered: 1/6/11
Re: (infinity) A real story
Posted: Oct 12, 2013 4:13 PM
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In article <9e886147-f862-4ce1-a7a1-0356919d5784@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> On Saturday, 12 October 2013 04:11:42 UTC+2, Ben Bacarisse wrote:
>

> >>> Yes, there are monotone sequences of set. Yes, what you say about them is
> >>> rubbish.

> >
> >> I only say about them that they are monotone sequences.
>
> > No, you said this of them as well:
>
> | The principle says that in a set of finite lines, there is always one
> | line containing all elements of the set. Simple as that.
> | And that priciple does not fail for infinite numbers of lines, because
> | every line has a finite number of elements.

> > You snipped it again, presumably
>
> because it is so obvious.


It is obviously false to anyone not imprisoned in
WM's wild weird world of WMytheology.
>
> > to avoid further exposure of this nonsense.
>
> ? Do you disagree with this principle in case of only finite lines?


WM's principle can only holds when he can present a specific and
concrete LAST line, which is not the case for WM's own example:

1
1 2
1 2 3
. . .

for which there cannot be a last line, as each line requires a successor.


> I am
> surprised.


You always claim to be surposed by those truths that you cannot admit.

>But since every non-empty subset of natural numbers has a first
> element,


But not necessarily a last one, and it is not the presence of a first
one but the neccessity of a last one which is at issue here.
Wm claims every non-empty list has a last element, which may well hold
in the obscurity of WM's wild weird world of WMytheology, but does not
hold anywhere else, not even in WM's own examples, like the one above.

> > You also refused (again) to answer the question it raises about the
> > sequence in question ({1}, {1,2}, {1,2,3}, ...). What's that, the sixth
> > time?

>
> That is a potentially infinite set.


Outside of WM's wild weird world of WMytheology all sets are either
finite or not finite, there is no third option.


> For every Z_n = (1, 2, 3, ..., n) there
> is a superset Z_(n+1). That is what people used to consider the only possible
> form of infinite sequences before Cantor appeared.


Then , even before Cantor, there must have been an endless sequence of
supersets, thus infinitely many of them, even if people were careful not
to mention it.
>
> > You also didn't provide any references to support the claim that this silly
> > principle is widely held, despite pretending that Zermelo and von Neumann
> > were among those that held it. Where do they say what you claim?

>
> Zermelo and v. Neuman applied inclusion monotonic sequences.
> Zermelo: { }, {{ }}, {{{ }}}, ...
> v. Neumann the somewhat more complicated { }, {{ }}, {{{ }}, { }}, ...


Did either of them claim, as WM does, that any such sequences must have
last members? If not then WM's citation DISPROVES his case.
>
> >> In particilar the finite initial segments of |N are a strictly
> >> monotonic sequence. Without any single exception.

> > They are indeed. I am surprised, then, that you can can't say which one
> > "contains all elements of the set".

>
> I told you more than once: There is no such beast like all elements of the
> set.


There is everywhere outsde of WM's wild weird world of WMytheology.
So what in WM's wild weird world of WMytheology prevents it there?
>
> > You've said "the set" is not N, and later you said that it is not an
> > infinite,

>
> I said, the set is not actually infinite. But it is potentially infinite. Is
> it really so difficult to understand?


Which set is that?

Note that it wold have to be a set which cannor have a successor larger
than itself, but if WM cannot even tell us which set that would be, how
can he claim that it even exists.
>
> >> You call that rubbish. I call it mathematics.
> > No. Did you read my words? They are up there for all to see but I'll
> > re-quote them again here:

>
> >>> Yes, there are monotone sequences of set. Yes, what you say about
> >>> them is rubbish.

> > See? I called what your made-up principle *says* about that sequence
> > rubbish. That the finite initial segments of |N are a strictly monotonic
> > sequence is not in question.

>
> And the result is what I said.


Not ever outside of WM's wild weird world of WMytheology.
>
> > Of course they form a strictly monotonic sequence. That's why your
> > principle applies to the sequence.

>
> And more is not existing. There is only the sequence to which this principle
> applies.


Everywhere else, if one has a sequnce of sets, which is just special
sort of a set of sets, one also has the union of that set of sets, which
must contain the successor of WM's "last member".
>
> (Please don't tell me again that it's not N, and that it's not an infinite
> set -- we'll be here for years if you keep saying what it isn't. I want to
> know what it *is*.)


Since WM cannot show us precisely what his "maximal set" is, we take
leave to doubt its existence.

We can always merely take the union of any set of sets, whether nested
or not, according to any and all standard set theories, so we have a
specific justification in standard set theory for our union but WM has
no such justification in any standard set theory for his "last set" of
an infinite sequence of sets.
>
> Here you are, explicitly: |N is potentially infinite.


Only in WM's wild weird world of WMytheology.
Everywhere else, it is actually infinite.

> There is for every n in |N an m in |N such that m > n.
> There is for every n = |{1, 2, 3, ..., n}|
> a larger m = |{1, 2, 3, ..., n, ..., m}|,
> but there is no aleph_0 = |{1, 2, 3, ...}|
> There is nothing like *all* n.


Then where do you get off relying for your argument on a setl ike |N
which is just what you say cannot exist.
>
> Proof: Inclusion-monotony otherwise would fail for finite sets already. That
> is impossible.


What WM claims as proofs are no more than poofs.
--






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