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

[Ariel Scolnicov <ariels@compugen.co.il>]

Marc Lehmann <pcg@goof.com> writes:


[...]

> the set of all strings is countable, the set of reals isn't.
> there are a lot of examples out there that prove that the integers are
> uncountable by extnding them with zeroes, for example.

No.  The integers are countable.  Even if you decide to write
"...0001" for "1", "...0002" for "2", ..., "...0042" for "42" etc.,
you still only get a countable set.  As you'd expect from a 1-1
mapping that is "onto".

The "standard" way to get uncountable sets is to allow infinitely
(countably) many non-fixed digits.  One way to do this is to go to
real numbers ("3.14159265...", "2.718281828459045..."); another is to
extend your digits to the *left* ("...5409548281828172"; these are
essentially Archimedes Plutonium's p-adics, but not all who deal with
them are quacks).

[This is somewhat unrelated to regular expressions, Perl or Fun; I'll
be glad to take any further discussion private, Marc]

[...]

-- 
Ariel Scolnicov        |"GCAAGAATTGAACTGTAG"            | ariels@compugen.co.il
Compugen Ltd.          |Tel: +972-2-5713025 (Jerusalem)	\ We recycle all our Hz
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