On 07/20/2012 01:11 AM, Steven D'Aprano wrote:
On Thu, 19 Jul 2012 13:50:36 -0500, Tim Chase wrote:

On 07/19/12 13:28, Chris Angelico wrote:
On Fri, Jul 20, 2012 at 4:20 AM, Tim Chase
<python.l...@tim.thechases.com>  wrote:
Sure it terminates...If you don't run out of RAM to represent the
number "i" in question, there's also this "heat death of the universe"
limit I keep hearing about ;-)

I'd be more worried about the heat death of your computer, it's likely
to be sooner. How many people have access to a computer that'll still
be running in ten years, much less a thousand?

Just putting a maximum bound on the problem, providing a time-frame in
which I can be fairly certain that the program will have terminated. :-)

I'm reminded of Graham's Number, which is so large that there aren't
enough molecules in the universe to write it out as a power tower
a^b^c^d^..., or even in a tower of hyperpowers a^^b^^c^^d^^... It was the
provable upper bound to a question to which experts in the field thought
the most likely answer was ... six.

(The bounds have since been reduced: the lower bound is now 13, and the
upper bound is *much* smaller than Graham's Number but still
inconceivably ginormous.)

You don't even need to go that high. Even a run-of-the-mill googol (10^100) is far larger than the total number of elementary particles in the observable Universe.

--
Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/
 San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Jabber erikmaxfrancis
  I think it is safe to say that no one understands quantum mechanics.
   -- Richard P. Feynman
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