Re: ******* TRY THESE SCI.MATH **********
From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 01/20/05
- Previous message: Martin Johansen: "Re: atoi"
- In reply to: |-|erc: "******* TRY THESE SCI.MATH **********"
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Date: Thu, 20 Jan 2005 14:56:35 -0500
Note: the word "random" is meaningless in these discussions.
"Arbitrary" is being substituted as part of the interpretations.
|-|erc wrote:
> Take any reasonable interpretration of the terms you can to get an answer where possible.
> If there is ambiguity, state all possible interpretations and answer each.
>
> "A random real number will be on a computables list to an infinite number of digits" True / False / Other
1) "An arbitrary real number will be on the list of computables" Other:
maybe
2) "Any prefix of an arbitrary real number will be on the list of
computables" True.
> ____
>
>
> "All finite subsequences of a random real number will be on a computables list" True / False / Other
"All finite subsequences of an arbitrary real number will be on the list
of computables" True.
> ____
>
>
> "All digits of a random real number are covered in all finite subsequences of that number" True / False / Other
1) "A list of all prefixes of an arbitrary real number can be
constructed" True
2) "A list of all finite subsequences of an arbitrary real number can be
constructed" True
> ____
>
>
> "If you have the list of computables, a random real number can be on it to an infinite number
> of digits, and yet not be on the list" True / False / Other
As stated: false. The real either is or is not on the list, but not both.
1) "If you have the list of computables, an arbitrary real number can
have all of its finite prefixes on the list, and yet not be on the list"
True
> ____
>
>
> How many digits of a random sequence have the prefix up to that digit
> occur on a member of any complete computable number list?
aleph_0 (all of the finite prefixes are on the list)
>
> Random Sequence =
> <593738..........................................................................................>
> |<--- How many of these digits satisfy the question? --->|
>
> UTM(row, col) mod 10
> 1 <23424............>
> 2 <54434............>
> 3 <59373.............>
> ...
>
> ____
>
> * remember : how many digits (of the random sequeence), not how many digits (fit on each row of UTM).
-- Will Twentyman email: wtwentyman at copper dot net
- Previous message: Martin Johansen: "Re: atoi"
- In reply to: |-|erc: "******* TRY THESE SCI.MATH **********"
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