Re: ******* TRY THESE SCI.MATH **********

rupertmccallum_at_yahoo.com
Date: 01/20/05 

Date: 19 Jan 2005 21:27:21 -0800

|-|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
> ____
>

I'm assuming your probability space is [0,1] with Lebesgue measure.

There is probability 0 that a random real from that space will be
computable.

>
> "All finite subsequences of a random real number will be on a
computables list" True / False / Other
> ____
>

True, every finite decimal is computable.

>
> "All digits of a random real number are covered in all finite
subsequences of that number" True / False / Other
> ____
>

Don't really know what this means. It's true that the finite segments
of a real number determine what that real number is.

>
> "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
> ____
>

A real number r can be such that for each natural number k, there is a
member of the list of computables such that r agrees with it to k
digits, yet r is not on the list.

>
> How many digits of a random sequence have the prefix up to that digit
> occur on a member of any complete computable number list?
>
> Random Sequence =
>
<593738..........................................................................................>
> |<--- How many of these digits satisfy the question? --->|
>

Every finite segment of a real will appear on the list of computables.

> 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).
>
> Herc
> --
> Have you now or have you ever been a member of the
antidisestablishmentarianism party?

Relevant Pages

  • YOU IGNORAMUSES ACTUAL:LY BELIEVE THIS ?
    ... >>are on the list of computables and you can move the bar any finite ... The bar will NOT, however, reach infinitely to ... At any point M_n in the sequence, the bar has only moved a finite ... Then it has moved to the right m digits, where m is in N. Then ...
    (sci.math)
  • Re: HOW MANY DIGITS OF PI HAVE PROPERTY X ?
    ... how many of those appear in some computables list? ... how many digits of an arbitrary sequence appear in some computable list? ... If ANY prefix of pi occurs in ANY element of Y,> then ALL SHORTER prefixes occur in the SAME element. ... > Pi ITSELF is computable, so if Y includes all computable> numbers, Pi ITSELF occurs ON THIS LIST AS A MEMBER OF Y.> THAT member gets it right for ALL digit-positions. ...
    (sci.logic)
  • Re: ******* TRY THESE SCI.MATH **********
    ... number of digits" True / False / Other ... computables list" True / False / Other ... member of the list of computables such that r agrees with it to k ...
    (sci.logic)
  • YOU IGNORAMUSES ACTUAL:LY BELIEVE THIS ?
    ... >>are on the list of computables and you can move the bar any finite ... The bar will NOT, however, reach infinitely to ... At any point M_n in the sequence, the bar has only moved a finite ... Then it has moved to the right m digits, where m is in N. Then ...
    (sci.logic)
  • Re: ******* TRY THESE SCI.MATH **********
    ... number of digits" True / False / Other ... computables list" True / False / Other ... member of the list of computables such that r agrees with it to k ...
    (comp.theory)