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. So it must distributed over at least two lines.
This can be accomplished for |N by two lines like
123 567... 1234 678...
or for (a, b, c) by two or three lines
ab bc ac
or by more lines. But we see that at least two elements a, b and two lines exist, such that there is a line with a and without b and a line witout a and with b.
> > 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.