On 2012-05-29, Aielyn <gjo1984@gmail.com> wrote: > Which does make me wonder, though... what would happen if you were > to construct a set by starting with an enumerable set, then find the > cantor diagonal and insert into position 1, then find the cantor > diagonal and insert into position 2, then find the cantor diagonal > and insert into position 3, then... you see where this is going, I > assume. The limit is, technically, well-defined
Indeed it is.
> but the cantor diagonal is, technically, also in the set, due to > the limit.
No, it isn't. You have a sequence of entries that converges toward the antidiagonal, but none of them are equal to it.
> Obviously, the problem is assigning an integer to it (and you could > just apply a permutation of finite extent and find a new cantor > diagonal)... but what properties would that set have, relative to > the initial enumerable set?
Nothing particularly special, as far as I can tell. The "lower triangle" of the list will be completely determined by the original list's diagonal digits and your antidiagonal function, and the "upper triangle" by the digits above/right of that diagonal.
