Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology § 255
Replies: 69   Last Post: Apr 24, 2013 9:49 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 255
Posted: Apr 24, 2013 9:24 AM

On 23 Apr., 23:03, Virgil <vir...@ligriv.com> wrote:

>
> > The question is whether there is a line with all nunbers of the
> > columns.

>
> That is a different question to which my answer is
> "No! There is no line with all the number of the columns."

If all numbers of the columns are in lines, but not all are in one
line, then there must exist at least two lines (or more) containing
all naturals, but containing not all in one line.

> > The union of the set of all lines is a line
>
> If that were so, then WM should be able to give us the number of that
> line.

No, there is no last natural number. Nevertheless every line is the
union of itself and all its predecessors. Unioning again and again
will not increase the number of elements.

{a, b, c} = U {a, b, c} = UU {a, b, c}.

Same holds for the lines.

> Actually, NO line is equal to the union of all preceding lines.

Every line is the union of itself and of all preceding lines.
> >
> > All that is contained in all lines collectively, is also contained in
> > one single line s_i.

>
> Which line would than be that contains the largest member of the next
> line ?

The next line.

> Which line, s_i, would it be that can contain i+1 ?

Is i+1 in the column? Can it be there without being in a line?
>
> > exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.
>
> If, for each natural number i, s_i = { n in |N: n <= i},
> then for every h in |N, (h in s_i) <==> (h <= i)
>
> Thus  WM's "m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k"
> says (m <= j) & ( m > k) & (n > j) & (n <= k)
> or   (m <= j) &  (k < m) & (j < n) & (n <= k)
> but (m <= j) &  (j <n) => (m < n)
> and (k < m) &  (n <= k) => (n < m)
> so in WOLKENMUEKENHEIM  one has n < n and m < m.

That proves that there is no aleph! Only if there are more natural
number of numbers in the first column than in every line, we need the
exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.

Regards, WM

Date Subject Author
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 David C. Ullrich
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Bergholt Stuttley Johnson
4/20/13 Virgil
4/20/13 fom
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 Virgil
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/20/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 Virgil
4/20/13 fom
4/20/13 Virgil
4/20/13 fom
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/20/13 fom
4/20/13 fom
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 Virgil
4/20/13 Virgil
4/20/13 Virgil
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 Virgil
4/21/13 mueckenh@rz.fh-augsburg.de
4/21/13 fom
4/21/13 Virgil
4/22/13 mueckenh@rz.fh-augsburg.de
4/22/13 Virgil
4/23/13 mueckenh@rz.fh-augsburg.de
4/23/13 Virgil
4/24/13 mueckenh@rz.fh-augsburg.de
4/24/13 Virgil
4/24/13 mueckenh@rz.fh-augsburg.de
4/24/13 Virgil
4/24/13 fom
4/23/13 gus gassmann
4/20/13 fom
4/20/13 fom
4/20/13 mueckenh@rz.fh-augsburg.de
4/20/13 fom
4/20/13 Virgil
4/20/13 Virgil