Search All of the Math Forum:

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

Topic: (infinity) A real story
Replies: 6   Last Post: Oct 12, 2013 6:03 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: (infinity) A real story
Posted: Oct 12, 2013 4:36 PM

mueckenh@rz.fh-augsburg.de wrote:

> On Saturday, 12 October 2013 06:14:55 UTC+2, Virgil wrote:
> > mueckenh@rz.fh-augsburg.de writes: > On Friday, 11 October 2013 15:27:19
> > UTC+2

>
> >> 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.
>
> Of course. That is the principle of inclusion monotony. How should it be
> else?

It would be better as a principle if it were true, but sadly , outside
of WM's wild weird world of WMytheology it is not true.
>
> > But that principle does not even hold for WM's own diagrams, like
>
> 1
> 1 2
> 1 2 3
> . . .
>

> > or
>
> 1
> 2 1
> 3 2 1
> . . .

> > In which no line can contain all members of all lines because only a last
> > line could do that, but there is no last line.

>
> Right. There is no infinite line.

Your diagrams require an actual infinity of finite lines to be complete
as indicated.

>
> > But every one of those infinitely many lines is a proper subline of its
> > next line, with no last line ever containing everything.

>
> You are right. No last line. No everything. What do you conclude? Apply to
> the authorities: Virgil desires that everything should exist. Therefore
> mathematics has to drop the principle of inclusion monotony?

Mathematics tends to drop any asssumptions when they contradict others
that mathematmics finds more valuable, and there are a lot of others far
more valuable to mathematics than WM's monotonous
"principle of inclusion monotony".
--

Date Subject Author
10/11/13 Ben Bacarisse
10/12/13 Virgil
10/12/13 mueckenh@rz.fh-augsburg.de
10/12/13 Virgil
10/12/13 mueckenh@rz.fh-augsburg.de
10/12/13 Virgil