27 Apr
2014
27 Apr
'14
9:29 p.m.
On Sun, Apr 27, 2014 at 6:22 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
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.
Ah, well I (as a constructivist) wouldn't say the set is non-empty, then. But I can see how if you are only able to construct two or more elements of each set, then there may not be a way to pick one. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com