Date: Mar 6, 2013 4:57 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
WM <> wrote:

> On 6 Mrz., 12:05, William Hughes <> 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.

Why not use the function vocabulary and call those lines
"values of L_m",
with a different value for each m in |N.

> But that
> is only a quarrel about word.

It is considerably more than that, since WM repeatedly tries to hide the
functional nature of L_m while WH repeatedly tries to reveal it.

> Nevertheless, you have not yet answered
> the more important question.

Why should WH have to answer every question when WM does not?
Or at least not successfully!

WM still has not successfully answered any of mine about the linearity
of functions from the set of all infinite binary sequences to the set of
all paths of a CIBT.

> Is there a particular reason? Remember,
> not long ago you claimed that potential infinity as well as actual
> infinity would yield the same results.

If there were any respectable axiom system for a set theory based on
potential infiniteness, one could hope that it would give similar
results as ZF or NBG or similar axiom systems of standard mathematics
give, but no such respectable axiom system allowing for merely potential
infiniteness appears to exist.

And where is WM's proof that some mapping from the set of all binary
sequences to the set of all paths of a CIBT is a linear mapping?
WM several times claimed it but cannot seem to prove it.