Re: "A random real number will be on a computables list to an infinite number of digits"

From: The Ghost In The Machine (ewill_at_sirius.athghost7038suus.net)
Date: 01/20/05 

Date: Thu, 20 Jan 2005 15:00:18 GMT

In sci.logic, George Cox
<george_coxanti@spambtinternet.com.invalid>
 wrote
on Thu, 20 Jan 2005 02:50:56 +0000 (UTC)
<41EF1C98.718BD804@spambtinternet.com.invalid>:
> |-|erc wrote:
>>
>> True / False / Other ?
>> ____
>>
>> "All finite subsequences of a random real number
>
> What is a random real number?

The quesion

"All finite subsequences of a random real number
are in a computable list L"

can be rerendered:

"What is the probability that, for an arbitrary element r of R,
that Prefix(r) is wholly contained in the computable list L?"

where Prefix(r) = {q: q = floor[r * 10^n]/10^n, n >= 0, n in J}.

AFAIK, this is a fairly general technique for dealing with
probability questions -- an extension of T/F questions. 

-- 
#191, ewill3@earthlink.net
It's still legal to go .sigless.

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