In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 17 Mrz., 00:30, Virgil <vir...@ligriv.com> wrote: > > > > > > We call it unfindable or unfixable > > > > > because as soon as we have found it, it is no longer the last line. > > > > > > If finding it makes it not what it is supposed to be, the how does one > > > > prove that any such thing exists? > > > > > Simply by observing that otherwise, there must be a set with at least > > > two natural numbers, both of which do not belong to the set. > > > > Non Sequitur, at least outside WMytheology. > > > > Where actually infinite set of naturls is allowed, nothing like what WQM > > demands is needed or even possible. > > In mathematics the assertion of existence of a non-empty set of > natural line-numbers implies that there is a least line-number.
Which, while true, is, as usual and as expected, irrelevant!
While there may be natural numbers which are, in some sense or other, unfindable, there is nothing which is simultaneously a natural number and has no successor natural number.
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.