Re: The Usual Heinlein Thing

On Thu, 06 Mar 2008 18:50:10 GMT, Wayne Throop <throopw@xxxxxxxxx> wrote:
::: But there are exactly as many transcendental numbers with names like
::: 5,327,458*pi + e^(gamma) as there are integers.

:: Only if you don't allow infinitely long names, or infinite charactersets.

What, you don't think there are infinitely many integers?

??

So, "infinitely long names" are already allowed.

Er, try again. A name's a list of characters. If you have only finitely long
names, there are as many of those (countable infinity) as there are integers.
If you allow infinitely long names, that pops you up to the power of the
continuum - whatever the cardinality of the real numbers is, and that's known
to be bigger than the integers' infinity.

Change that to "*and* infinite character sets", and you might h ave something.
Maybe. But pretty definitely not just with one or the other.

Definitely just with one, though I see I made a mistake - a countably infinite
character set with finitely long names is still the same cardinality as the
integers. But countably-infinitely-long names with a finite character set
leaps you past that cardinality (see: Cantor).

Dave
--
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It's not the clock that slows the hour The definition's plain for anyone to see
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