Re: How many digits is pi computable to?

From: Michael Mendelsohn (invalid_at_msgid.michael.mendelsohn.de)
Date: 01/17/05 

Date: Mon, 17 Jan 2005 18:53:16 +0100

Bill Smythe schrieb:
> "|-|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?
>
> Or, instead of using a countability argument (but still assuming the number
> of sequences is countable and each sequence is countable), you can construct
> a new sequence of coin flips as follows:
>
> If the first flip by the first person was heads, define the first flip in
> the new sequence to be tails, and vice versa.
>
> If the second flip by the second person was heads, define the second flip in
> the new sequence to be tails, and vice versa.
>
> Et cetera.
>
> That way, the new sequence will be different from the Nth previous sequence
> at the Nth flip. Hence, the new sequence will be different from all the
> previous sequences.

IIRC Herc rejects any kind of diagonalization argument.
(Maybe that has changed, though.)

Cheers
Michael 

-- 
Still an attentive ear he lent        Her speech hath caused this pain
But could not fathom what she meant   Easier I count it to explain
She was not deep, nor eloquent.       The jargon of the howling main
                 -- from Lewis Carroll: The Three Usenet Trolls

Relevant Pages

  • Re: No Unique Initial Segment And No Characteristic Expansion
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  • Re: No Unique Initial Segment And No Characteristic Expansion
    ... its infinite, no hyperinfinity just because you can't understand the 1 to 1 map ... > We don't HAVE to have a diagonalizer, LET ALONE an anti-diagonalizer, ... whatever the mth flipper's first flip was. ... the "1st flips sequence", ...
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  • Re: No Unique Initial Segment And No Characteristic Expansion
    ... random flippers are doing is NOT 1, ... that visits each of Herc's Infinite flippers once and asks, NOT, "what ... was your nth flip", but rather, "what was your first flip?", and ... THIS SEQUENCE IS NOT UNIQUE *EITHER*, ...
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  • Re: How many digits is pi computable to?
    ... >> An infinite amount of people each flip coins infinite times each. ... of sequences is countable and each sequence is countable), ... If the second flip by the second person was heads, ...
    (comp.theory)
  • Re: How many digits is pi computable to?
    ... >> An infinite amount of people each flip coins infinite times each. ... of sequences is countable and each sequence is countable), ... If the second flip by the second person was heads, ...
    (sci.math)
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