Re: just 5 quick answers then I can summarise and GO

From: John Savard (jsavard_at_excxn.aNOSPAMb.cdn.invalid)
Date: 01/10/05 

Date: Mon, 10 Jan 2005 19:09:42 GMT

On Tue, 11 Jan 2005 03:12:08 +1000, "|-|erc" <h@r.c> wrote, in part:

>A)
>SEQUENCE = <314159265..........................................................................>>
>
> <--- HOW MANY DIGITS???--->

The decimal expansion of pi contains an infinite number of digits.

>(B)
>COMPUTABLES
>1 <398498498.................>
>2 <484849848.................>
>3 <383873838.................>
>..
>
>How many digits of (A) appear in correct sequence in (B), guaranteed?
>
>1 _______

Pi is computable. But even for a real number, or infinite sequence of
digits, it is guaranteed that, for any finite number N you pick, however
large, you can find an entry in the list of computable numbers that has
the first N digits of the sequence in the correct order, starting from
the beginning.

Thus, there is no digit in the infinite sequence so far to the left in
(A) that you cannot find an element of (B) that matches the sequence *up
to that digit*.

But the infinite sequence in (A) _itself_ is still not guaranteed to be
a member of (B), only an infinite number of sequences approaching it
arbitrarily closely.

>===================================================
>
>
>(A)
>RANDOM SEQUENCE = <654445676764545..............................................................>
> <--- HOW MANY DIGITS???--->
>
>(B)
>COMPUTABLES UTM(row, col) mod 10
>1 <398498498.................>
>2 <484849848.................>
>3 <653873838.................>
>..
>
>How many digits of (A) appear in correct sequence in (B), guaranteed?
>
>(Randomness could be introduced from outside the computer).
>
>2 __________
>
The answers are the same as for the case above, with the exception of
the reference to pi being computable.

>===================================================
>
>
>So given a coin sequence <HTHHHTTHTTHTHTHTHHHTH.......................>
>
>How many flips (at least) of cs appear on the computable number list in order?
>
>CNL = UTM(row, col) mod 2
>
><0010101010100101..>
><1010110110101001..>
><0000000000000000..>
><1111111111000000..>
><1010101010101010..>
>..
>
>3 __________
>

Again, the answers are the same as for the case above.

>==================================================
>
>
>> >> all coin sequences are computable to infinite length ?
>>
>> false

Yup, that's the answer.

>4 = "all coin sequences to infinite length appear (all flips in order) in any UTM computable list."
>
>4 <-> _________

No, they do not.
>
>=======================================================
>
>>
>> >What about this one, any Cantorians want to assign it T or F?
>>
>> >"There is a maximum to the number of coins in any given oo coin sequence, that can be computed"
>>
>> false too

Yup, that's the answer.

>What is the opposite as a true proposition?
>
>5 ___________________________________________
>
For any infinite coin sequence, even if that sequence is not itself
computable, any finite subset of that sequence, no matter how long, is
computable.

John Savard
http://home.ecn.ab.ca/~jsavard/index.html

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