On Mar 6, 12:48 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 6 Mrz., 12:05, William Hughes <wpihug...@gmail.com> wrote: > > > > L_m is a single line if m is a natural number. > > > Would you prefer to call L_m infinitely many lines? > > > Nope, I would prefer to call L_m a function > > (of time and person). A function may have as > > value a "single line of the list" > > but calling something that changes a "single line of the > > list" is silly.- > > I said always that L_m is a function (of several arguments) and that > this function takes as vaules lines of the list. As it takes single > lines, I don't see why we should not call them single lines.
Because calling L_m a single line is certain to cause miscommunication and using language in a way certain to cause miscommunication is silly.
So the statement
"there is no line which contains every FIS of d"
becomes in the language of Wokenmuekenheim
"there is no findable line which contains every FIS of d"
Similarly, there is no statement about the behaviour of "actually infinite" sets that does not have an analogue in the language of Wolkenmuekenheim.
in Wolkenmuekenheim you would say (about potentially infinite sets)
A subset K of the lines of L contains every FIS of d iff K has no findable last line.
to mean the same thing as the statement (about "actually infinite sets")
A set of lines K contains every FIS of the diagonal iff K has infinite cardinality
This is what I mean when I say that "potential infinity" behaves like "actual infinity".