27 Apr
2014
27 Apr
'14
6:23 p.m.
Nope. You can prove a set is nonempty without constructing any elements.
How?
For example, let S be the set of well-orderings of the reals. This is non-empty, but you can't construct any of its elements. A slightly more sophisticated example is the compact Hausdorff space betaN \ N of non-principal ultrafilters. Sincerely, Adam P. Goucher