On 06/01/2011 08:51 PM, Shane Hathaway wrote: > On 06/01/2011 02:27 PM, Aaron Toponce wrote: >> Similar proofs can be constructed for any countable set: > > Related to this, I've been wondering why irrationals are not considered > countable. Is it not true that for any irrational number, a computer > program can be written that converges to that number as the number of > iterations reaches infinity? Any computer program can be represented as > a large integer, so computer programs are countable, and by extension, > any number that a computer program can represent (but not necessarily > produce) ought to be considered countable.
Well, that would mean infinity is countable, since it's trivial to write a program that always increases. Infinity is uncountable, so I wonder where the logic broke. Shane /* PLUG: http://plug.org, #utah on irc.freenode.net Unsubscribe: http://plug.org/mailman/options/plug Don't fear the penguin. */
