In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 23 Apr., 22:40, Virgil <vir...@ligriv.com> wrote: > > In article > > <1c4b9840-ec9c-47cf-b825-bbd9df7fa...@a3g2000vbr.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 23 Apr., 16:35, fom <fomJ...@nyms.net> wrote: > > > > On 4/23/2013 3:59 AM, WM wrote: > > > > > > > 1 > > > > > 2, 1 > > > > > 3, 2, 1 > > > > > ... > > > > > > WM is an unabashed ultrafinitist > > > > > No. There is no largest number. > > > > That's our line! > > And there are not aleph_0 natural numbers. > > > > But there are numbers larger than any natural number. > > > > The number of naturals is such a number. > > Then this number of numbers must be in all lines without being in one > single line.
If this number of natural numbers is larger than every natural number, as you concede above, then it is clearly NOT a natural number, and thus has no business appearing in any list of only natural numbers.
If WM wants non-natual numbers to appear in his lines, there are lots of negative integers and non-integral rationals he can stick in them, and even more irrationals.
> So it must distributed over at least two lines.
As an obviously non-natural number, it need not appear in any line of only natural numbers. >
> > > > Every element of the first column is in a line. There is no actually > > > infinite line. > > > > That may be in physics, but does not hold in mathamatics, in which a > > line may be extended beyond every finite point. > > In physics we cannot prove anythig like that but just in mathematics > we can prove that it is impossible.
In mathematics, WM has repeatedly shown that WM is unable to prove even the simplest of things. Though he does claim quite a lot that he never manages to prove, much of which is false in any standard mathematical arena. --