The Princeton Companion to Mathematics has a good description of this starting on page 572. Basically the proof goes like this: Define a random variable that c

The Princeton Companion to Mathematics has a good description of this starting on page 572. Basically the proof goes like this: Define a random variable that can only take on integer values. Show that the expected value is less than one. The random variable must therefore sometimes take on the value of zero. If your random variable was defined to mean something interesting at zero, then the above is an existence proof. What they mean by "non-constructive" is that you still don't actually have an example of the thing existing -- you just know it does. Very cool.