I believe the definition they are using is something like: given a random process X for your percent return, if you invest in n nths of your money into iid copi

I believe the definition they are using is something like: given a random process X for your percent return, if you invest in n nths of your money into iid copies of X, you will get the same expectation, but with smaller variance compared to putting it all into one copy of X. That's diversification.