In article <a028808d-6576-454b-9feb-2caa4d325876@v1g2000yqn.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 14 Okt., 23:51, Virgil <vir...@ligriv.com> wrote: > > There is nothing to "preserve". Here we have three > > > sequences B(n) = H(n) = R(n). If one of them has a limit, then all > > > have limits. > > > > Two of them may exist, but the third (bottom) side cannot exist unless > > there is a last line to be that side, which there isn't. > > None of them may exist other than as suprema. That means that Cantor's > diagonal argument fails in my special list
Logic fails in your special list. > > 0.0 > 0.1 > 0.11 > 0.111 > ... > > Here is another limit example: > > LIM[n-->oo] {0, 3, 6, ..., 3n} > LIM[n-->oo] {1, 4, 7, ..., 3n+1} > LIM[n-->oo] {2, 5, 8, ..., 3n+2} > > Do only two of these limits exist?
As these do not in any way answer my objections, they are irrelevant. > > The infinite triangle can be constructed by just these numbers: > > a > > a > bb > > c > ac > bbc > > d > dc > dac > dbbc > > > d > dc > dac > dbbc > eeeee > > and so on in an obvious way.
Things become very much unobvious in your triangles after the 26th one.
