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.