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Topic: (infinity) A real story
Replies: 9   Last Post: Oct 16, 2013 9:08 PM

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: (infinity) A real story
Posted: Oct 12, 2013 4:25 PM
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In article <070c8685-8bde-4ddc-9b71-93058e60463c@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> 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.


Possibly because, unlike WM, they understood everything that required
undestanding about "nclusion monotony", in particular, the the principle
that Wm caims does not hold anywhere outside of WM's wild weird world
of WMytheology.
>
> 1
> 1, 2
> 1, 2, 3
> ...
>

> >> 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.


It seems to fail quite stndardly everywhere outside of WM's wild weird
world of WMytheology.
>
> > 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.


It is everywhere outside of WM's wild weird world of WMytheology,
>
> > BTW, I suggested this alternative long ago and you rejected it.
>
> In mathematics actually infinite sets simply do not exist.


They do everywhere outside of WM's wild weird world of WMytheology.
>
> >> I said, the set is not actually infinite. But it is potentially
> >> infinite. Is it really so difficult to understand?


That you lie? No!


> > 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.


Potential nifinity doe not exist at all, as it is, at most, only
potential, not actual.

In actual mathematics, things which are only potential never exist, as
they canot be both only potential and actually actual.
>
> > Can it refer to a potentially infinite set?
>
> Cantor has no copyright on set (Menge).


Neither has WM. And clearly WM's notions of set theory are incompatible
with anyone else's.
>
> > I can't see how it can include potentially infinite sets,
>
> But actually infinite sets do not exist in mathematics at all.


Wm can only speak for what goes on in WM's wild weird world of
WMytheology, not what goes on outside it, since he imposes axioms and
assumption in his WMytheology that no one else accepts.
>
> > > 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. 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.


Then it is clearly WM who needs the psychiatrist, since he is the one
claiming that which all others reject.
>
> Regards, WM

--





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