In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 3 Mrz., 21:54, Virgil <vir...@ligriv.com> wrote: > > In article > > <4c166e24-d4f0-44a8-9ca7-0b379218b...@w3g2000vba.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 2 Mrz., 23:18, Virgil <vir...@ligriv.com> wrote: > > > > > > So that in WM's world there is a largest natural number whose value is > > > > variable and dependent on many factors, so that it may sometimes be > > > > increasing and sometimes decreasing. > > > > > The alternative is a completed infinity that allows for a union of > > > subsets that contains more than all its proper subsets. > > > > That may occur in Wolkenmuekenheim, but not in standard mathematics. > > So all natural numbers are in the list > 1 > 1, 2 > 1, 2, 3 > ... > > But not all natural numbers are in one single line? > Hence, they must be in more than one line. TND?
Right! But all naturals are in any infinite set of lines.
And the union of any infinite set of lines is d. > > On the other hand, it is proven, that there are never more than one > line required to contain all that is contained in several lines.
WRONG! AS USUAL!
While what is contained in any set of lines WHICH HAS A LAST LINE is contained in that last line, when one is outside of Wolkenmuekenheim, MOST sets of lines do not have a last line, and no such set has all members of all its lines in any one line.
> Contradiction. This falsifies actual infinity.
NO, it merely falsifies WM's inanity. > > > > > > And we have a contradiction with analysis. Compare "The Paradox of > > > > > Tristram Shandy", PlanetMathOrg (2012) > > > > > > Only fools like WM ever expect Tristam to finish recording his whole > > > > life. > > > > > The same fools expect by the same argument that all rational numbers > > > can be enumerated. > > > > Since such a complete ennumerations have often been completely > > described, and are part of the standard literature, WM will have to show > > which rationals such ennumerations fail to ennumerate before he can > > justify his counterclaim. > > And which parts of Tristram's life are not described in his diary?
Until it is proved that Tristam Shandy is now dead, one cannot assume that he is not still writing it. And I defy WM to produce Shandy's death certificate. > > Regards, WM --