Re: How many digits is pi computable to?

From: |-|erc (h_at_r.c)
Date: 01/18/05 

Date: Tue, 18 Jan 2005 15:32:40 +1000

"Ed Murphy" <emurphy42@socal.rr.com> wrote in
> On Tue, 18 Jan 2005 11:59:33 +1000, |-|erc wrote:
>
> > Infinite people each flip coins infinite times. Can you always find a
> > different sequence of heads and tails?
>
> [snip diagonal argument]
>
> > its really quite simple, infinite people all doing the same thing you are
> > doing dispells any possibility of you being unique.
>
> "Infinite" is insufficiently precise; some are larger than others.
>
> P = number of people
> C = number of coin flips per person
> S = number of possible sequences of coin flips
>
> C is countably infinite, but S is uncountably infinite.
>
> If P is countably infinite: ./
> * It can't cover all of S.
> * Your comment is false.
> * The diagonal argument works.

Say you have an (countable) infinite set of people, and they only toss coins a finite number of times.

<<sample>>
P C
1 HTHT
2 HHTT
3 TTHH
4 TT
5 H
6 T
...

they are given the constraint to only toss 4 times maximum.

you can construct any sequence you want once I show you the list, but
first you have to tell me how long your sequence is going to be?

Herc

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