Peter said:
It is a very surprising turn of events.
Not really.
Peter, you are on a completely wrong track.
For one thing there is the claim of the so called 'Halting Problem':
No such function can exist.
And then there is the proof for this claim:
Based on the assumption that such a function exists, it can be shown
that this assumption leads to a contradiction: namely that the function
cannot exist.
But note: The proof you are attacking is based on the *assumption* that
such a function exists.
So when you attack the proof, and turn it around, all you end up with is:
Based on the assumption that such a function exists, that function can be
written.
That's not nearly of the same quality as the original proof. If I assume
the moon consists of chesse, then I can conclude that the moons material
is cheese. Fine. It's all based on the assumption. But: If I can proove
that even if I assume that the moon is made of cheese the only conclusion
is that it is not made of cheese, I have shown something important: No matter
what I do or assume, the moon cannot be made of cheese.
You should familiarize yourself with proofing methods in a better way. The
type of proof used for prooving that Halting problem can only be used to
show that X does not exist. It always works the same way
* 1) assume X
* 2) show that assuming X leads to a contradiction. You can use X in that
proof
* 3) only logical conclusion: -> X cannot be assumed
If you need to show that X really exists, you need a different type of proof.
Just fighting step 2) in the above is not enough.