Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 203
Posted:
Feb 1, 2013 8:19 PM
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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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