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

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: (infinity) A real story
Posted: Oct 12, 2013 12:14 AM
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mueckenh@rz.fh-augsburg.de writes:

> On Friday, 11 October 2013 15:27:19 UTC+2, Ben Bacarisse wrote:
>> mueckenh@rz.fh-augsburg.de writes: > On Thursday, 10 October 2013
16:35:29
>
>> Yes, there are monotone sequences of set. Yes, what you say about
>> them is rubbish.

>
> 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.


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.

>| And that priciple does not fail for infinite numbers of lines,
>| because every line has a finite number of elements.


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






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