Date: Feb 1, 2013 8:19 PM
Author: Virgil
Subject: Re: Matheology � 203
In article

<eb5eb732-89c0-4009-a071-6ebc4fc40c9e@h2g2000yqa.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 1 Feb., 16:18, William Hughes <wpihug...@gmail.com> wrote:

> > Let a potentially infinite list, L,

> > of potentially infinite 0/1 sequences

> > have the property that every

> > (in the sense of "all from 1 to n")

> > potentially infinite 0/1 sequence

> > is a line of L

>

> I just gave an example. Do you agree? Or do you think of something

> else?

> >

> > Let s be a potentially infinite

> > 0/1 sequence.

> >

> > Does this imply that there is

> > a natural number m, such that s

> > is the mth line of L

> > ?

>

> Would you please notice that "all" in the sense of "from 1 to n"

> simply means "all lines that are in the list". Of course they are in

> the list. Not more and not less. Why the heck should some other,

> external line that is not in the list, be in the list?

But is the last line in the list? NOTE that a set with a first line and

for each line a successor line different from all its predecessors is

necessarily ACTUALLY infinite.

>

> Hint: You try to ask for a 0/1 sequence of the set of all possible 0/1

> sequences. My answer is: There is no set of all possible 0/1

> sequences. Therefore your question is meaningless in potential

> infinity.

But still meaningful in standard mathematics, in which a set is either

actually infinite or actually finite, but never so neurotic as to be

unable to tell which.

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