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

From: John Savard (jsavard_at_excxn.aNOSPAMb.cdn.invalid)
Date: 01/09/05 

Date: Sun, 09 Jan 2005 20:33:21 GMT

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

>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

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

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