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

From: Timothy Little (tim-via-n.i.net_at_little-possums.net)
Date: 01/07/05 

Date: 7 Jan 2005 06:13:01 GMT

|-|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"

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.

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?

- Tim

Relevant Pages