Date: Mar 6, 2013 7:18 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots
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".