> On 2010-06-28, Virgil <Virgil@home.esc> wrote: >> It does not require that any element in the listing be known, but >> correctly tells what to do for any listing > > I think that is even a bit too informal for Peter. The phrase "tells > what to do" is superfluous, all that is mathematically required is > that existence of an antidiagonal sequence for each list is proven. > He's going to latch onto "tells what to do" and think that it means > that there is an algorithm for everything involved. > > Witness his confusion over the example I defined of a list where each > entry was computable but the list itself (and its antidiagonal) was > not. He didn't dispute that the list *existed*, but considered it > cheating because he couldn't use the definition to extract actual > digits of the antidiagonal - it didn't "tell him what to do" in his > own special sense.
Ah, you're right, of course. I'll revise that part.
Don't get me wrong. I'm not in this to "educate" anyone or to correct misconceptions. I'm mostly in this for the practice, both at working with various proofs and at identifying misconceptions. If anything useful comes of it for someone else, all the better, but I won't feel bad if people exit this thread thinking exactly as they came into it.
(Unlike Virgil, I'll eventually get bored and go away. :)