In article <email@example.com>, WM <firstname.lastname@example.org> 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 alternaive 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.
In standard mathematics there is no natural which is not a member of a finite initial set of naturals, so the union contains only those naturals that are in some finite initial, and therefore proper, subset.
Only in such places as Wolkenmuekenheim can it be utherwise.
>That is > obviously a contradiction with mathematics.
Only with the corruption of mathematics that WM is trying to sell.
> It is as wrong as the > claim that the list > 1 > 1, 2 > 1, 2, 3 > ... > contains all natural numbers in the first line, not so obvious a > contradiction though for people who lack logical capabilities.
Outside of Wolkenmuekenheim, every line of that list contains all the number in the first line. > > > In the world of the majority, it is your potential infiniteness, not our > > actual infiniteness, that is self contradictory. > > In the world of people who lack logical capabilities many amazing > things can happen.
We have often noted how WM's lack of logic leads him to claim amazing, and false, things. > > > > In our world every natural is required to have a successor, whereas in > > WM's world there must always be a natural not having any successor, > > though no one can say which one it is. > > > > > But there are all FIS of d, which must be in infinitely many different > > > lines of the complete list. > > > > if there are all of them, > > There cannot be all.
Until WM can tell us precisely which ones cannot be, we shall continue to reject his claims. > > > > > > > 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.
> > > > > > > > > Two proofs against actual infinity. In addition there is the Binary > > > Tree which has not more than infinitely (aleph_0) paths that can be > > > distinguished even by infinite strings (with aleph_0 bits each). > > > > > > But the set of all such paths has uncountably many paths that one will > > never be able to list. > > Since infinite paths do not exist other than by finite command.
If the COMPLETE INFINITE BINARY TREE can exist at al, then those paths all exist. too.
And WM has conceded that existence by his claim of having a linear mapping from the set of all binary sequences to the set of paths of a Complete Infinite Binary Tree. --