[r-t] Re: Extension, etc.

Chris Poole poole at maths.ox.ac.uk
Mon Nov 15 14:28:02 UTC 2004

On Mon, 15 Nov 2004, Don Morrison wrote:

> Sorry to distract from the main subject of discussion here for
> something hairsplitting, but....
> On Mon, 15 Nov 2004 09:04:07 -0000, Robin Woolley <robin at robinw.org.uk> wrote:
> > ii) The MC says "in most cases an extension that works for two stages of
> > extension works for an indefinite number of stages". The fact that we have
> > been given one example of where it doesn't work suggests that there are
> > others - dare I suggest an uncountably finite set.
> What does "uncountably finite" mean?
> 1) is it just something humoursly non-sensical, a mathematical joke
> for saying "well, it's not infinite, but it's big and complex enough
> that no one can in practice count it"?
> 2) a typo for "uncountably infinite" -- that seems unlikely, since it
> would at first thought appear that there are probably only a countably
> infinite set of methods possible (and only a finite set for stages
> below any given stage, for example a billion bells or fewer)
> 3) or something else entirely?

>From the context of the sentence, I interpret this a finite set of unknown
dimension N (and N is sufficiently large such that it's pretty tricky to
work out what it is!).


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