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

From: |-|erc (h_at_r.c)
Date: 01/07/05 

Date: Fri, 7 Jan 2005 16:23:21 +1000

"Timothy Little" <tim-via-n.i.net@little-possums.net> wrote in
> |-|erc wrote:
> > What about this one, any Cantorians want to assign it T or F?
>
> I can only guess what you mean by "Cantorian".
>
>
> > "There is a maximum to the number of coins in any given oo coin
> > sequence, that can be computed" [1]
>
> You still haven't defined "coin sequence". I'll choose to interpret
> it as "binary sequence" which is a well-defined mathematical term that
> seems to be what you mean. It's still an ambiguous proposition since
> you haven't ordered the existential and universal quantifiers, but
> fortunately it's false either way. It's still unrelated to what is
> meant by a computable infinite sequence.

Can you state the correct negative form of proposition 1?

>
> Here are two propositions. See if you can tell the difference:
>
>
> (A) "For any sequence <a_n>, there exists a program P, such that for
> any natural number N, P(n) = a_n for all n < N"
>
> This says "All sequences are computable to infinite length"
>
>
> (B) "For any sequence <a_n>, for any natural number N, there exists a
> program P, such that P(n) = a_n for all n < N"
>
> This says "All sequences are computable to finite length"
>
>
> The difference is the reversed order of the existential and universal
> quantifiers. It is a very important difference. Do you understand
> the difference?
>

yes, I've formulated these 2 myself in about 1000 posts over 3 years here, ask ghosty!

but I've already told you they are the same, since they are both true. if you
want a concrete difference you'll have to be more selective than any_program.
I do realise that conventional text mathematics they are not both true, but they are,
if you find a valid example of a sequence in one not the other let me know.

Good Luck!

Herc 

--
what do women say about male sperm?  sex cells never age?   protein rich?
     :-C==8  You'll never never know if you never never blow!   :-C==8

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