Re: Uncomputable Natural Numbers


The infinite case is not confirmable.

On Sep 4, 1:38 pm, reaste...@xxxxxxxxx wrote:
Neither is the finite case.

It IS SO TOO, dumbass.
You can adopt CONVENTIONS.
You can just DECREE that when such and such a string occurs, THE INPUT
IS JUST *OVER*.

And WE HAVE so decreed.


 THAT IS WHY WE NEED
to make the ASSUMPTION that the input is finite.  That assumption
is in fact made in the usual TM paradigm.

We don't need to assume the input is finite.

BUT WE *DO, ANYWAY*.
If you don't, then the amount of trouble you get into REALLY IS great
enough
that you will find that YOU DID need to, AFTER all. My point is, we
are only
TRYING to compute with finite programs on finite inputs. Yes, other
paradigms
of computation are possible, but for purposes OF THIS discussion, WE
JUST
DON'T GIVE A *** about any of that, because THIS paradigm is IN FACT
ADEQUATE
to computing anything that people can compute.


We can prove the SC can only read finite strings.


No, obviously, BY DEFINITION, you CAN'T prove that UNLESS you have
ALREADY MADE ASSUMPTIONS that IMPLY that, in other words, unless
you are being completely circular. Besides, if you have something
that can only
read finite strings in any case, why are you alleging that it can't
confirm that its
input is finite? Anything that was on the input tape that it DID NOT
read, and that does not affect, nor ever had any potential chance to
affect, the computation, IS NOT part of the input to the computation!

My proof shows we can never assume the SC
nevers halts.

That is ridiculous.

We can never assume the SC halts if there
is a symbol the SC will halt on.
Since there are always unread symbols
on the input tape, there is always the possibility
the "halting" symbol has not been read yet.

Of course, but that is why, precisely as I said, YOU CAN confirm THE
FINITE case.


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