One day I was trying to prove the Cauchy Schwarz inequality using the rearrangement inequality. However, at last I succeeded in proving it. Assume that and are sequences of real numbers. Here are my steps:
Step 1: Let
Step 5: So by rearrangement inequality, we have :
Step 8: Squaring both sides, we have:
Step 9: By replacing A,B we restore the form and we get the famous Cauchy Schwarz Inequality:
If you think I made a mistake in the proof, click the step number where I made a mistake. If you think that my proof is valid, click .