Let be a vector in . Prove that .
I am not sure how to start this. I'm guessing I need to use induction but I don't know how.
Let where .
Therefore, you want to prove .
We will prove this in a geometric way. Imagine a right triangle with legs . The third leg is by Pythagorean theorem. However, by the triangle inequality it means the sum of any two sides must be great than the third sides, therefore, . Can you prove your vector inequality now?
Yes, that makes sense to me, and I was able to prove the rest. Thank you.
I am having difficulty with the proofs in this class :/ I have never had to do proofs before. I can do them for the homework by studying the book and getting help from others, but today I had a test and didn't do well. There were 4 proofs, and I was only able to do two and most of the third, before running out of time.
Do you know of a book or some other resource to help me get more practice? My book has some proofs (not many), yet my professor is almost entirely focused on proofs. I can understand when she writes them on the board but that is completely different from inventing my own.