Re: [FWP] japhy had a silly idea...

["Robert C. Helling" <helling@aei-potsdam.mpg.de> (by way ofowner-fwp@technofile.org)]

>From fwp-l Tue May 29 02:28:39 2001

On Mon, 28 May 2001, Abigail wrote:

> Well.... only if you match against finite strings. However, regexes
> can match infinite strings as well. And since there is an obvious,
> 1-to-1 mapping between the set of reals between 0 and 1 and the set of
> strings (including the infite length strings) consisting of digits only,
> and each such a string is matched by /^\d+$/, it's not true that a set
> matched by a regex is of countable size.

OK, fine, we might allow for infinite strings. What about the RE itself,
can it be inifinite, countably or even uncountably, like

/^A$|^AA$|^AAA$|^AAAA$.../

or

/AAAAAAAAAAA...|BBBBBBBBBBBBBBBBBBBB...|CCCC....|.../

Or the other way round: A RE that matches the comma separated list of all
prime numbers. Or:

We learned in the discussion, that we can represent all reals in [0,1] by
inifinite strings. What about inifinte subsets of [0,1]. Like: Find a RE
that exactly matches a subset of [0,1] that is no Lebesque measurable
(Hint: This smells like the axiom of choice)

Have fun
Robert

-- 
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Robert C. Helling        Institut fuer Physik
                         Humboldt-Universitaet zu Berlin
print "Just another      Fon +49 30 2093 7964
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