In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 17 Mrz., 22:39, William Hughes <wpihug...@gmail.com> wrote: > > You are contradicting yourself. > > > > You say there are no necessary findable lines > > because of the last line (an unfindable line) > > In pot. inf. there is always a last line.
But as every line implies the actual existence of a successor line, no such last line can exist ong enough to be seen.
> It is unfindable or > unfixable.
> But I do not wish to discuss potential infinity but actual infinity > here. > > > > You say that if a set of lines contains an unfindable > > line it is necessary that there are > > two findable lines. > > No. I say that in actual infinity a list contains all natural numbers. > But they cannot be in one line, because there is no actually infinite > line. This is a contradiction.
Only if one claims that a FISON need not be a FISON. > > Please kindly note: Even if my personal theory was self-contradictory
Which it is!
> that would not improve the situation presently adopted in mathematics. > So please concentrate on defending your position.
We define the set of naturals so that it has a unique first member and for each member there is a successor member larger that that predecessor.
According to that definition, all WMytheology is nonsense.
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.