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Re: Re: Creating a Random Function to Select an Irrational


On 3 Aug 2009, at 18:45, BenT wrote:

>  Although I am not
> interested in cryptograpy or statistic probabilities for which
> "random" numbers are typically used, if not "relied" on, my biggest
> concern, that your use of WorkingPrecision partly addresses, is the
> prevention of repeating digits within the "random" value which would
> imply some sort of "rationality" to the number.

Of course you can get any number of repeated digits in a finite  
expansion of an irrational number. Look for example at the last 6  
digits of this:

N[Pi, 768]

(actually, these last digits should all be 9, as you see by looking at  
N[Pi, 769]].

If you go long enough you will find a repeating sequence of any length  
(to get 7 successive repeated digits you need to take a total of  
710107 digits of Pi).

Thus, there is no advantage in using finite expansions of symbolic  
irrationals over using RandomReal with high WorkingPrecision.

Andrzej Kozlowski



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