That's all we have to do? All the examples we did in class had 2 - 4 cases we needed to prove (based on the definition of absolute value and the problem in question) in order to make this work.
That's all we have to do? All the examples we did in class had 2 - 4 cases we needed to prove (based on the definition of absolute value and the problem in question) in order to make this work.
Yes. You could prove (a) by cases (assume is positive and is negative, etc.) but it's unnecessary if you know that .
For the other two proofs, all you need to know is that is a metric, and then you can use properties of metrics to complete the proof. No cases required!