On 13 Okt., 07:20, Brrrrains <kiwisqu...@gmail.com> wrote: > On Oct 12, 4:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 12 Okt., 20:53, Virgil <vir...@ligriv.com> wrote: > > > > > > Actually its width MUST be larger than every line > > > > > But its width is spanned by the lines. There is nothing more. > > > > The width of such a triangle can only be spanned by its last line, if > > > any, since every other line is necessarily shorter, thus not spanning > > > the entire width. > > > > So when the triangle does not have a last line, as WM insists, there is > > > nothing left to span it. > > > That is correct. That is potential infinity. But by R(oo) = B(oo) then > > there is no finished infinity of digits or symbols in the diagonal. > > > And there is not a complete set of all natural indices. > > > > Only in WMstadt is the set of all natural numbers in any way > > > problematical. In standard mathematics, it is one of the standards. > > > And as we see, it falsifies the old mathematical theorem, that > > Forall n in |N: H(n) = B(n) = R(n) > > implies H(oo) = R(oo) = B(oo) > > if existing > > If H(n) = B(n) for all n, then > > lim n->oo H(n) = lim n->oo B(n) > > if the limits exist. > > That is not a theorem, but a statement that two identical sequences of > real numbers have the same limit. > > But H(oo) is not lim n->oo H(n). B(oo) is not lim n->oo B(n). > > So there is no theorem that says H(oo) = B(oo) > > In fact, since there is no well-defined definition of H(oo), B(oo), or > R(oo), everything you are writing is in fact, a complete non sense.
You never heard the expression limit ordinal? Or heard it, but never wondered why omage has been called limit ordinal? Or do not believ that omega can be a limit? Or think that geometry is not mathematics?
Grenze ist immer an sich etwas festes, unveränderliches, daher kann von den beiden Unendlichkeitsbegriffen nur das Transfinitum als seiend und unter Umständen und in gewissem Sinne auch als feste Grenze gedacht werden. (Cantor)
