In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 26 Feb., 13:11, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 26, 12:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > We both agree > > > > There does not exist an m > > such that the mth line > > of L is coFIS with the diagonal > > (here we interpret "There does > > not exist" to mean "we cannot find"). > > > > So we agree any such m must be an > > unfindable natural number. > > > It is a variable that can take any natural number. > > > I am not interested in arguments > > about whether an unfindable number exists. > > > > [I still do not understand why > > WM rejects the obvious proof by contradiction > > I do not understand why WH rejects the obvious proof by contradiction > that all natural numbers of the list are in one line together.
Probably because outside of WMytheology it does not qualify as a proof at all. > > > > Suppose that P is a predicate such that > > for every natural number m, P(m) is true. > > > > Assume a natural number, x, such that P(x) > > is false exists. > > For every natural x, the proposition "P(x) = there are more than one > line necessary to contain all natural numbers from 1 to x of the list" > is false.
For every natural n, there is a finite set containing all naturals less than to equal to n. But this in no way includes all naturals, which, outside of WOLKENMUEKENHEIM is a perfectly legitimate set.
There are even models for it, like the von Neumann naturals in ZF, which WM does not like but cannot refute.
But if, as in WM's model, if x is not equal to 1, there must be lines prior to the x line, so one line alone can only contain one natural. > > > call it k > > Then P(k) is both true and false. > > Contradiction, Thus the original assumption > > is false and no natural number, x, such > > that P(x) is false exists) >
> > Every natural number is findable. "The number of the last line of the > list" or "the last natural number" are simply variables that can take > natural numbers as values. But these values cannot be fixed, known, > found.
Then they do not represent natural numbers at all.
The very definition of the set of natural numbers prohibits either "The number of the last line of the list" or "the last natural number" from being variables that can take natural number values, just as "C" in "The circle C" cannot take squares as values. --