In article <email@example.com>, firstname.lastname@example.org wrote:
> 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?
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". --