28 Apr
2014
28 Apr
'14
6:07 a.m.
There's the old example of whether the set X of [irrational pairs (a,b) such that a^b is rational] is nonempty. Set a = b = sqrt(2). If (a,b) is not in X (i.e., a^b is irrational), then setting c = a^b and d = sqrt(2) shows that (c,d) is in X. --Dan Mike S. wrote: ----- Adam G. wrote: ----- . . . You can prove a set is nonempty without constructing any elements. ----- How? -----