> Am Mittwoch, 5. Februar 2014 17:41:13 UTC+1 schrieb Ben Bacarisse: >> >> If they gave the >> "obvious" construction based on the bijection f: N -> P that the path >> p(n) "goes the other way" to the path f(n)(n) does would you mark them >> down? > > They would know that also the other way is already realized, for every > n, in a rationals-complete list. And they would know that this > rationals-complete liste is realized by the Binary Tree. You cannot > cope with them.
You don't teach them how to tell if two infinite sequences are the same or not? After a course from you, they could no longer show that the sequence defined above is not equal to any sequence in the image of f? You are not doing them any favours.
Anyway, it seems that your "of course" was premature. You've seen that it leads to a result you don't want and you are now back-tracking. If they argued as I suggested you'd tell them they are wrong. Shame on you.