In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 24 Mrz., 22:35, Virgil <vir...@ligriv.com> wrote: > > > > > The theorem does not cover what will transpire when two or more lines, > > along with all their predecessors, are removed. > > There is no reason to remove more than one line with all its > predecessors
There is no reason to pay any attention to WM's claims here either, as they all assume situations contrary to fact, at least in standard mathematics.
Though WM does claim that in they hold in some evanescent neighborhood of his person called Wolkenmuekenheim, though not by WM. . > > > > So it is of some interest to note that for any set of lines having a > > maximal line in it, > > Does induction
Since WM snipped the sense out of my line, I feel justified in returing the favor. > > > > > It is easy to see we know what > > > > will happen if we remove a natural > > > > number of finite lines. > > > > > > However, we do not know what will happen > > > > if we remove an infinite number of > > > > finite lines. > > > > > That's why we use induction. > > > > Except that no inductive argument will go from removing a finite set of > > lines to removing an infinite set of lines, > > Induction holds for the infinite set of naturals and for the infinite > set of lines.
Lets see WM's statement of the inductive principle.
One acceptable form is:
There exists a set of objects, N, and a zero object such that 1. Zero is one of the objects in N. 2. Every object in N has a successor object in N. 3. Zero is not the successor object of any object in N. 4. If the successors of two objects in N are the same, then the two original objects are the same. 5. If a set contains Zero and the successor object of every object in N, then that set contains N as a subset.
And any form which cannot be shown to be equivalent to the above form is unacceptable as an inductive principle.
And the forms which WM has been hawking cannot be shown to be equivalent, so are unacceptable. --