On Saturday, 12 October 2013 06:14:55 UTC+2, Virgil wrote: > email@example.com 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?
> 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.
Right. There is no infinite 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.
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?
Alas, in matheology your wish has already been granted, and in mathematics, there are no authorities who could grant your wish.