## Calculus (3rd Edition)

Since $-|a| \le a \le |a|$ and $-|b| \le b \le |b|$, then by addition we have $-|a|+-|b|\le a+b\le |a|+|b|$ $-(|a|+|b|)\le a+b\le |a|+|b|$ This can be rewritten as: $|a+b|\le |a|+|b|$ which is the triangle inequality.