Infinity

[Shane Hathaway]

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