scott wrote:
> But the probability of 0.5 turning up is not zero, it is 1/infinity.
> Sometimes they can be used interchangably, but in this situation they
> cannot.  You won't find a mathematician that claims 1/infinity
> universally is equal to zero under all circumstances in normal number
> systems.
> 
> On the other hand, writing an infinite sum like 1/2+1/4+1/8+.. does
> *exactly* equal one, always, never with any doubt, it is universally
> accepted in mathematics.

	Sorry, but no - the explanation doesn't work. If you read my original
long post, you'd see that the two cases are *identical*.

	Getting a sequence of all heads forever is identical to picking a point
from 0 to 1. Both have probability 0. There's a 1-1 correspondence
(which I showed earlier) between the two. They're not just similar -
they're the same.

	Conversely, saying that a tails _must_ appear in a sequence is just
doing 1 - (1/2)^n, and taking the limit to infinity, giving 1. Which is
the same as saying that the probability that I _won't_ pick 0.5 when I
choose a number between 0 and 1 is 1.

	I even forget how the 1/2 + 1/4 + 1/8 sequence enters the picture - was
that the result of some probability calculation?
	
>>  Explain to me the exact mechanics which force the works to appear.
> 
> Calculate the probability, you will find it is equal to one.  Exactly
> one. That, by definition, means it is guaranteed, or "forced" if you
> like, to happen.  QED.

	Yes, by *definition*.

	Warp asked for mechanics. Invoking mathematics is not invoking any
physical reasons. The mathematicians have merely defined it that way.
Which does not mean it will happen.

-- 
"The security of the Enterprise is of Paramount importance.


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