Re: How many digits is pi computable to?
From: |-|erc (h_at_r.c)
Date: 01/18/05
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Date: Tue, 18 Jan 2005 11:59:30 +1000
"Bill Smythe" <chichess@beforeRCNafter.com> wrote in
> "|-|erc" wrote:
> > The question (5 months ago) was.
> > An infinite amount of people each flip coins infinite times each.
> Can you
> > come up with a new sequence of flips?
>
> If both instances of "infinite" above mean "countably infinite", then I'd
> say yes. The total number of coin flips so far is countable times
> countable, which is still countable. The number of possible countably
> infinite coin flips is 2 to the countable, which is uncountable.
>
> Bill Smythe
>
Consise argument, but does it contradict John's proposition?
"if you have the list of computables,
a random real number will be on it to an infinite number of digits"
i.e. every possible coin sequence is on the list of computables to an infinite number of flips.
> > How many numbers are in this sequence?
> > <1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ....>
>
> aleph_0
>
> >
> > How many numbers are in this sequence? (duplicates allowed)
> > <3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 6, ....>
>
> aleph_0
Right
How many flips of this random sequence <HTHTTTHTTTHTHTHHHTHT..>
make an appearance after all their predecessors in (members of) this list?
UTM(row, col) mod 2
1 <0101101000..>
2 <1110101000..>
3 <0000000000..>
4 <1111100000..>
..
You can use an alphabet substitution you deem appropriate.
Herc
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