Mueen Nawaz wrote:
> 	See, in mathematics, everywhere I've seen infinity used with rigor (and
> where I understood it), behind all the formalism is basically a
> definition of what they mean. Sometimes it is intuitive, but there's no
> guarantee that it will conform to reality.

Given that, as far as we know, the universe isn't infinite, I'd go so far as 
to say there's a decent guarantee that it *doesn't* match the universe. :-)

> universal truth in the "real" world - it's just a consequence of how we
> define cardinality (and numbers).

Sure. Understood. The monkey thing is obviously not a "real world" thing.

> 	I won't accept that I can't get a forever continuous string of heads
> from a coin unless someone can give me a _physical_ reason. There isn't
> any - there's only a mathematical one.

You can't get a forever continuous string of heads from a coin because as 
far as we know, there's no such thing as forever. :-) Fair nuff.

>> But I think I've exhausted my ability to convince you that Shakespeare
>> necessarily appears in the output, if the output is infinite and making
> 
> 	Well, perhaps we're just playing semantic games.

I hadn't realized you were trying to talk about "really" outside of 
mathematics.  I think we're in complete agreement.

> 	I'm simply wary of using a _purely_ mathematical argument to make
> statements about the real world.

I agree. Math is only useful to the extent it's isomorphic to reality, which 
is impossible to prove mathematically. It's pretty amazing that so much of 
reality seems to conform to simple rules once you ignore the right stuff.

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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