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. IN infinite sets "not all x" is a triviality, because "all x" is a faslity. Even the set "all natural numbers have divisor 1" is wrong, because there is no thing named "all natural numbers". Every natural number can be divided by 1 without remainder. "Every natural number is positive." Correct. "All natural numbers are positive." False. At least completely meaningless like "tutum trara is blue".