In article <firstname.lastname@example.org>, email@example.com wrote:
> On Saturday, 13 July 2013 00:46:52 UTC+2, Zeit Geist wrote: > > > Zeit Geist 00:46 (9 hours ago) > >> Each natural belongs to a finite initial segment. None of them requires a > >> number that is larger than every natural number. In fact the contrary. If > >> you do not talk about the set, then there is no reason to talk about > >> alephs. > > > > > >Yes, but for every Natural there is a larger natural, > > > which belongs to a finite initial segment
Which finite initial segment is always only a part of a larger finite initial segment as infinitum. > > > hence the number of Naturals is larger than any Natural. > > Why wouldn't I talk about the set of Naturals? > > because the result would be self-contradictory:
Only in WM's wild weird world of WMytheology, where infinite sequences are all finite. > > All naturals are every column of the list > > 1 > 21 > 321 > ...
But not , even though WM claims it, in any row of that list.
> So all naturals are in the list.
But not, even though WM claims it, in any row of that list.
> Everything that is in the list is in one line of the list.
Every number that is in the list is in some line of the list, but for every line in the list there are members of the list not in that line.
> Proof for mathematicians: The lines are inclusion monotone.
Which only proves that the limit (union) of the sequence of lines is not a line. Outside of WMytheology, the limit of a strictly increasing infinite sequence cannot ever be a member of the sequence.
WM'a quantifier dyslexia strikes again: true: for every n in |N there is a FISON F such that n is in F, false: there is a FISON F such that for every n in |N, n is in F. --