Cauchy–Schwarz inequality

The Cauchy–Schwarz inequality is like a little rule that helps you compare two numbers. Say someone gives you a pair of numbers, say they give you 3 and 4. You can use the Cauchy-Schwarz inequality to compare these two numbers. The Cauchy-Schwarz inequality says that if you multiply the two numbers together, then the result must be less than or equal to the square of the bigger number. So if you take 3 and 4 and multiply them together you get 12. The square of 4 (which is the bigger number) is 16. So 12 is less than 16, so that's okay - the Cauchy-Schwarz inequality is happy.