On Oct 13, 10:37 am, WM <mueck...@rz.fh-augsburg.de> wrote: > 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) > > Regards, WM-
The above is an old-old ""trick"" by WM: when he cannot push further with his nonsenses, then he cuts&pastes something in german, which can or cannot be remotely related to the gist of the discussed point but in most cases says nothing about that gist, and thinking (figure of speech) that if something was said by someone then it MUST be very important for someone. Becasue, you know, actual mathematicians (i.e. people who know Cantor's Proof is correct logically) "believe" that mathematicians like Cantor, Hilbert or Russell never erred...:>)
The above parraph in german could be translated as "Limits are always something fixed, stable (immutable, unchanged), and therefore, between both concepts of infinity, only the transfinite could be thought also as fixed under certain circumstances and in some sense"
Now ask yourself: what had good-ol WM in mind when he began asking about ordinals and limit oridnals and stuff IN THIS convo? Or simpler: what had this good chap in mind when he posted the above parraph? The simplest, and perhaps most accurate answer, is: nothing, he just can't tell apart between cardinals and ordinals. Perhaps he also tried to confuse people by bringing over something unrelated to the discussion...who knows?
