Date: Oct 12, 2013 2:12 PM
Author: Ben Bacarisse
Subject: Re: (infinity)  A real story writes:

> On Saturday, 12 October 2013 18:19:34 UTC+2, Ben Bacarisse wrote:
>>> Zermelo and v. Neuman applied inclusion monotonic sequences.
>>> Zermelo: { }, {{ }}, {{{ }}}, ...
>>> v. Neumann the somewhat more complicated { }, {{ }}, {{{ }}, { }}, ...

>> I note you give no citation, so I can't check that these titans of the
>> field agree with the nonsense you've posted about such sequences.

> Above you see their widely known formulation of the natural
> numbers. They did not think about the problem of inclusion monotony,
> probably because they did not imagine the set in the form of my table.

Ah, so that's a "no" is it? You can't cite anywhere where they agree
with this:

| 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.

(context the "lines" are sets -- elements in a sequence with Sn+1 > Sn.)

It does not seem to be widely accepted as you thought.

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

>> So the principle fails in this case.
> In mathematics this principle never fails. It is too obvious.

You just said it failed. You said "There is no such beast like all
elements of the set". If that is the case, how can there be "one line
containing all the elements of the set"? The principle says there is
*always* such a line.

You alternate between asserting P and ~P. In the posts where you assert
P you snip that part where you just said ~P, and vice-versa.

>> In other words, it says nothing at all about the case in point.
> Wrong. It says that the case in point is not a case in mathematics.

Interesting technique. Snip the explanation (was it too persuasive?),
leave the summary and simply state that it's wrong. Do you have no
reply to the argument?

For anyone still reading: WM does not indicate where he has removed
text, so it looks like he is addressing the points made. In fact, he
replies just to the bits that he can edit into something that looks like
a set of assertions. He can then just say it's all wrong, making it
look like tit-for-tat.

>> BTW, I suggested this alternative long ago and you rejected it.
> In mathematics actually infinite sets simply do not exist.

Great. I've said that's fine by me -- I'll go along with that to learn
what mathematics really is.

To what set does the principle refer in it's opening statement? It's
not an actual infinite set, but what is it in the case of Sn={i<n}?

I'm aware that you've just said that "the case in point is not a case in
mathematics" but since the principle is one of mathematics, but that
would mean it has nothing to say about this non-mathematics case. Can
you clear up, once and for all, whether the principle does indeed apply
to Sn as defined above?

If it does not apply, case closed (except to complain about the time you
wasted posting examples to which it does apply). If it does apply, the
fact that this case is "not in mathematics" hardly matters. It applies
so it makes a true statement about Sn and you can tell me what "the set"
is about which it makes its true statement.

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

>> Yes it is. But a couple of questions will clear it up in no time.
>> In the grand principle, does the term "the set" include or exclude
>> potentially infinite sets?

> According to Cantor "set" does exclude potential infinity. Potential
> infinity exists only in analysis.

I wanted to know your answer. Do I take that this statement reflects
you own view?

>> Can it refer to a potentially infinite set?
> Cantor has no copyright on set (Menge). That term was adapted from the
> German everyday language by Bolzano.

And another unmarked snip! And, guess what? It's that part that has the
question you won't answer. I won't repeat it again since I've asked it
above. You can snip it from that as easily as from anywhere else.

>> I can't see how it can include potentially infinite sets,
> But actually infinite sets do not exist in mathematics at all.

>> > There is nothing like *all* n.
>> Ah, the deductive rule known as "but". Let me see if I can apply it
>> correctly: there is for every n = |{1, 2, 3, ..., n}| a larger m, but
>> there *is* an aleph_0 = |{1, 2, 3, ...}|. Did I use it correctly?

> No.

I asked if I used the "but" deduction rule correctly, not if the
conclusion was correct. Here, I'll use it again:

> If there was an aleph_0, then it must be either in one line of the
> matrix or in two or more lines. But it cannot be there. If you had not
> yet studied mathematics, you would see it immediately. It is not a
> mathematical problem, but only a psychological one.

but you are wrong. See? That's how you used it in your definitive,
absolutely irrefutable, "proof", of something no one but you has every