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Re: Matheology § 203
Posted:
Feb 4, 2013 7:05 AM
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On 4 Feb., 12:33, William Hughes <wpihug...@gmail.com> wrote:
> This does not prevent us from using induction to show that
> there is no natural number n, such
> that the nth line of L contains every FIS
> of 0.111....
Of course. For every FIS in line n we can find a larger FIS. But there
are not all.
>
>
> > > Can a potentially infinite list
> > > of potentially infinite 0/1
> > > sequences have the property that
> > > if s is a potentially infinite 0/1
> > > sequence, then there is a line, g, of L
> > > with the property that every
> > > initial segment of s is contained in g
> > > ?
>
> > > Yes or No please
>
> > No.
>
> So we have potentially infinite sets like |N
> where you can say
>
> If L is a potentially infinite list of
> natural numbers then can have the property
>
> If n is a natural number then n is a line of L
or if FIS(n) is finite, then it is a line of L
>
> and potentially infinite sets like
> the potentially infinite 0/1 sequences
or the potentially infinite FISs (1, 2, ..., n) of |N
> where you cannot say
>
> If L is a potentially infinite list
> of potentially infinite 0/1 sequences
>
> then if s is a potentially infinite
> sequence then s is a line of L
or if |N is potentiall infinite, then |N is a line of L.
Yes, infinity is never finished.
Regards, WM
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