Proof by cases, part 2 (Screencast 3.4.2)

This video looks at another example of proof using cases, this time with real numbers and the absolute value function.

[jorossbarredo]

I love how you explained why proof by cases is the best technique to use here

[kolerhcp]

Thank you for this. I am currently taking IB HL math and these videos are awesome. I have a crappy teacher so I bought some books and couldn't check my results for this since there is no answer for these kinds of questions in the textbook( people should start writing the proof at the back of the book just for you to check sometimes). And your other videos about proof are also really awesome. I hope I can score a 7 on the exams next year just by studying by myself.

[mxlexrd]

The only slight mistake is when you said a ≥ 0 and b < 0 means ab < 0. In fact it should be ab ≤ 0. It doesn't really matter, but it's important to be precise when doing proofs.

[Wyui]

thank you this is a great video :D

btw may I ask and pls answer it :)

in the 2nd and 3rd um, why |-a| = (-a)? I mean it's an absolute value right? anything inside absolute value became positive number as far I known.... Explanation pls :D