Triangle inequality applied to subtraction?
So I checked out other questions and it appears my specific question wasn't answered
I was wondering if the following is valid: $$ \lvert a - b \rvert \le \lvert a \rvert + \lvert -b \rvert = \lvert a \rvert + \lvert b \rvert \\ \therefore \; \lvert a - b \rvert \le \lvert a \rvert + \lvert b \rvert $$
Thanks in advanced!
Solution 1:
Yes, that's valid. You may also be interested in the reverse triangle inequality.
Unfortunately, the reverse triangle inequality does nothing to reverse triangle inequality:
(from Brown Sharpie)