In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 28 Feb., 22:29, Virgil <vir...@ligriv.com> wrote: > > > > > You think that describing this situation as > > > > "there is a line which contains all FISs > > > > of d" > > > > is sensible. > > > > > Every FIS of d. > > > > In standard languages, including both English and German, > > "not all x" and "not every x" both require existence of an x which is > > not whatever is under discussion. > > These languages are not suitable to talk about mathematical infinity.
They are the languages used by most English speaking and German speaking mathematicians in this world.
> IN infinite sets "not all x" is a triviality, because "all x" is a > faslity.
In every standard set theory, one cannot have a set at all without having all of it. Thus whatever WM allows to go on in WMytheology is not any form of set theory.
> Even the set "all natural numbers have divisor 1" is wrong
Not outside WMytheology.
> because there is no thing named "all natural numbers".
There is outside of WMytheology. If there is an unambiguous rule for telling whether a test object is a natural nor not, then there is a set of ALL the objects satisfying that test. At lest everywhere outside of WMytheology.
> "All natural numbers are positive." False.
Only if one includes 0 as a natural, as in the von Neumann naturals.
> At least completely > meaningless like "tutum trara is blue".