Re: OPPOSITE OF all coin sequences are computable to infinite length ?

From: |-|erc (h_at_r.c)
Date: 01/10/05 

Date: Mon, 10 Jan 2005 10:31:01 +1000

"John Savard" <jsavard@excxn.aNOSPAMb.cdn.invalid> wrote in
> On Fri, 7 Jan 2005 12:35:09 +1000, "|-|erc" <h@r.c> wrote, in part:
>
> >> Is this TRUE?
> >> all coin sequences are computable to infinite length ?
>
> false

all coin sequences to infinite length, appear (each flip in same order) in any UTM computable list.

>
> >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

Then what is the opposite?

>
> It is FALSE that all coin sequences are computable to infinite length,
> but it is TRUE that _some_ coin sequences can be computed to infinite
> lengths.
>
> The number of infinitely long coin sequences has the cardinality of the
> continuum, and, thus, there are more of them than there are integers.
> There are only as many infinitely long coin sequences that can be
> computed (i.e., the binary expansion of pi) as there are integers.
>
> John Savard
> http://home.ecn.ab.ca/~jsavard/index.html

Herc

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