Re: countability of reals
From: Barb Knox (see_at_sig.below)
Date: 01/21/05
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Date: Fri, 21 Jan 2005 16:03:34 +1300
In article <3437ggF4766d1U1@individual.net>, "|-|erc" <h@r.c> wrote:
>> Every coin sequence is computable to infinite length.
>
>None of you are worth the collective bits in usenet that hold your posts
>
>until you ascertain the truth value of the above proposition.
You never did directly address the issue that if EVERY binary sequence is
computable then that means the halting problem is solvable: given any
enumeration of TMs, SOME binary sequence correctly maps each TM-index ->
{0,1} where 0 means that the TM with that index doesn't halt on a blank tape
and 1 means that it does.
If every sequence is computable than THAT sequence is computable. Oops.
>In article <crhrcd$tle$1@lust.ihug.co.nz>, Barb Knox <see@sig.below> wrote:
>
>>In article <3437ggF4766d1U1@individual.net>, "_|erc" <h@r.c> wrote:
>>
>>>> Every coin sequence is computable to infinite length.
>>>
>>>
>>>None of you are worth the collective bits in usenet that hold your posts
>>>
>>>until you ascertain the truth value of the above proposition.
>>
>>I have ascertained it's truth value, and it's False.
>>
>>(I don't know why I bother, but) let's suppose it's true that every infinite
>>binary sequence is computable. Then Chaitin's Omega sequence is computable,
>>which solves the halting problem. Oops.
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