> On Friday, 11 October 2013 15:27:19 UTC+2, Ben Bacarisse wrote: >> email@example.com 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 . . .
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. --