Some of the previous answers have said that sometimes the easiest way to prove a set it non-empty is to show that it's large or even infinite. A variation on that idea is to show that something exists by showing that the probability of selecting it at random from some larger set is positive. As one of my professors used to say, some things are so hard to find that the best way to look for them is at random.
John D. Cook
- 5.2k
- 1
- 48
- 72