Date: Feb 3, 2013 10:20 PM
Subject: Re: Matheology � 203
WM <email@example.com> wrote:
> On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote:
> > > > We can say "every line has the property that it
> > > > does not contain every initial segment of s"
> > > > There is no need to use the concept "all".
> > > Yes, and this is the only sensible way to treat infinity.
> > So now we have a way of saying
> > s is not a line of L
> > e.g. 0.111... is not a line of
> > 0.1000...
> > 0.11000...
> > 0.111000....
> > ...
> > because every line, l(n), has the property that
> > l(n) does not contain every initial
> > segment of 0.111...
> But that does not exclude s from being in the list. What finite
> initial segment (FIS) of 0.111... is missing? Up to every line there
> is some FIS missing, but every FIS is with certainty in some trailing
> line. And with FIS(n) all smaller FISs are present.
But with no FIS are all present.
> > Is there a sensible way of saying
> > s is a line of L ?
> There is no sensible way of saying that 0.111... is more than every
How about "For all f, (f is a FIS) -> (length(0.111...) > length(f))" .
It makes perfect sense to those not permanently encapsulated in