In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 18 Mrz., 00:59, Virgil <vir...@ligriv.com> wrote: > > In article > > <ba28932b-ac48-4567-8e5c-a7e9262f8...@z4g2000vbz.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 17 Mrz., 21:48, Virgil <vir...@ligriv.com> wrote: > > > > > > Mathematical truth is independent of time. > > > > > In fact??? Amazing! After Cantor's list has been diagonalized, it is > > > possible to include all diagonals into the list. But someone has > > > forbidden to change the list after time t_0 when the diagonalizers > > > start to do their work. > > > > Why does WM claim that after what WM calls "Cantor's list" has been > > diagonalized, he can include all anti-diagonals, when it is always > > possible to find others that have been so far overlooked? > > > > After each anti-dagonal of any list is found, prefix it to that list and > > then the anti-diagonal to the new list is not in the new list or the old > > sub-list. > > > > This procedure always finds new lines which are non-members of any of > > the prior lists of lines including all lines of any original list and > > all previously found anti-diagonals of those prior lists. > > Every list yields another diagonal.
So that as soon as any list exists, a non-member of that list is proved to exist, so the very existence of a list proves its incompleteness.
> And every diagonal can be included in another list. > > Both these facts are the two sides of infinity. Cantor did that false > step to choose one as more justified than the other.
The issue is whether a list can be complete in the sense of containing every possible sequence.
You concede that the very existence of a list demonstrates the existence of a diagonal not listed in it.
Thus one must conclude that no such list can list everything. > > With same right he could have argued that there are more even than odd > non-negative integers, because 0 is even and after every odd integer > there follwos an even one, just overlooking that after every even > integer there follows an odd one.
On CAN conclude that there are at least as many evens as odds from your argument, but not that there are more of them.
To conclude that there are more of one type than another one would have to show not only that the supposedly smaller set injects into the supposedly larger but the supposedly larger set does NOT inject into the supposedly smaller.
At least in the sort of proper mathematics that goes on outside of WMytheology. What goes on inside of WMytheology is entirely up to WM.
WM has frequently claimed that HIS mapping from the set of all infinite binary sequences to the set of paths of a CIBT is a linear mapping.
In order to show that such a mapping is a linear mapping, WM would first have to show that the set of all binary sequences is a linear space (which he has not done and apparently cannot do) and that the set of paths of a CIBT is also a vector space (which he also has not done and apparently cannot do) and then show that his mapping, say f, satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of the field of scalars and x and y and f(x) and f(y) are arbitrary members of suitable linear spaces.
While this is possible, and fairly trivial for a competent mathematician to do, WM has not yet been able to do it.