In article <email@example.com>, firstname.lastname@example.org wrote:
> On Monday, 14 October 2013 21:42:19 UTC+2, Virgil wrote: > > >> You must give a smallest line required. > > > You must prove that there is as smallest line reequired, but there isn't. > > If there is a subset of lines required, together containing more than each of > them, then it has a smallest one. If there is no smallest one, then there is > no such subset.
The set of all odd numbered lines will contain all members of all lines. The set of all even numbered lines will contain all members of all lines.
But these two sets of lines are disjoint, showi nt than no particular smalest line is ever required, so that WM's claim is false!
Similarly, given any set of lines tha contains al members of all lines, the same set minus its first line still does so, so that no particular first line is ever needed. > > > The set of odd numbered lines suffices, but so does the set of even > > numbered lines. > > Simple assertion of nonsense.
If it were really nonsense then there would have to be some number in the diagram which did not appear in ANY odd numbered line or some number which did not apear in any even numbered line. Which numbers of your diagram, WM, do not appear in ANY odd numbered line? Which numbers of your diagram, WM, do not appear in ANY even numbered line?
Unless you can name some such number, WM, your argument falls flat on its sku=inny ass. > > > Since these two sets of lines have no lines in common, there can be no > > particular line that is required, > > and there can be no such subset.
You mean that in the set of all lines, each line being numbered by its largest member, there is no such thing as the subset of all even numbered lines , or of all odd numbered lines?
Everywhere outside of WM's wild weird world of WMytheology both subsets exist, > > > It is impossible that two or more lines contain more than one of the lines. > > By induction we can prove that this is true for every set of finite lines. > Otherwise there would be a first line not obeying this rule.
But since no finite set of lines can cover more than its last line, no finite set of lines can cover all members of your diagram, but any and every infinite set of lines does so entirely. > > > But it is possible, and is the fact, that any and every infinite set of > > lines contains every natural in WM's diagram, > > That is neither fact nor possible
It is both everywhere outside the hellhole of anti-mathematics of WM's wild weird world of WMytheology. --