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Topic: Matheology § 293
Replies: 44   Last Post: Jun 27, 2013 2:25 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: WMytheology � 293
Posted: Jun 21, 2013 5:18 PM

mueckenh@rz.fh-augsburg.de wrote:

> muec...@rz.fh-augsburg.de wrote:
>

> > Re: WMytheology § 293
> > In article
> > WM <muec...@rz.fh-augsburg.de> wrote:
> >

> > > On 19 Jun., 23:38, Virgil <vir...@ligriv.com> wrote:
>
>

> >>> {1}, {1,2}, {1,2,3}, ... is a proper subset of |N, unioning all of them
> >>> cannot give any more than |N.

> >
> >> Certainly not more, but a lot less.
>
> >So, if, according to WM, the union of all FISONs does not include
> > all of |N, then WM must be claiming that there are natural numbers not
> > in any FISON.

>
> You should understand that logical proof is meaningless in case of a

Which understanding makes all of WM's claimed logical proofs invalid.
>
> Every natural number that anybody has used or ever will use belongs to a
> FISON, such that aleph_0 numbers must follow which are never used and cannot

SO that WM is claiming that there are naturals not in any FISONs?
>
> Therefore it is a contradiction to accept a set of natural numbers that has
> more than any finite number of elements.

wild weird world of WM's WMytheology.

What WM does inside that world is no part of mathematics, and very
little standard mathematics ever makes the transition into that world
unwarped.
>
> >
> >> The sequence of sets is inclusion-monotonic. This means there are never
> >> two
> >> or more sets the union of which surpasses each of the sets.

>
>

> > That only holds for unions of finitely many FISONs, but there are
> infinitely many FISONs.
>
> That holds for inclusion monotonic sets. The number of elements does not play
> a role.

It does if that number is not a finite number. Which it is not.
Every finite natural number necessarily and by definition has a
successor larger than itself.

So that WM's model in which this is not allowed is not allowed outside
the wild weird world of WMytheology.
>
> The infinite set (1/2^n) is strictly monotonic. Your arguing would allow that
> its limit is 100 and its sum is 1000.

Not at all.
Since the sequence, 1/2^n, is strictly decreasing, only a fool like WM
would evaluate its limit as being any greater than any one of its terms.
>
> > Any and every union of infinitely many FISONs includes all of |N,
>
>
> The sequence contains only sets each of which lack aleph_0 natural
> numbers.

But it contains a list of aleph_0 sets each of which contains one
natural not contained in any previous set in the list.
>
>

> > The sequence of FISONs contains aleph_0 FISONs, and any and every union
> > of aleph_0 FISONs contains all of |N.

>
>

> >> Lacking infinitely many natural numbers cannot be compensated by unioning
> >> infinitely many of such deficient sets.

>
>

> > It can, and does,
>
> That would require that a union after infinitely many unions

NOt if one's first union uses up any set of infinitely many FISONs, as
the leaves no naturals unused.

> That is not
> acceptable.

It is totally acceptable everywhere outside the minuscule