<email@example.com> wrote in message news:firstname.lastname@example.org... > On Saturday, 12 October 2013 04:11:42 UTC+2, Ben Bacarisse wrote: > >>>> 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. > | And that priciple does not fail for infinite numbers of lines, because > | every line has a finite number of elements. >> You snipped it again, presumably > > because it is so obvious.
Yet it is wrong: that principle does not fail for a potentially infinite set of finite lines because the set in question is (already) the limit of a sequence, and the limit entry is the line that contains all lines. The same by extension to the actually infinite, i.e. still with appeal to basic notions.