Why is it called the triangle inequality?
The triangle inequality is one of the most useful properties in calculus and analysis, which essentially says that going the longer way around a triangle is longer than going around the shorter way. Pretty easy right! But often times its much easier to go around the longer way, which helps us learn about the shorter path.
Check out my epsilon-delta arguments here which involve a couple triangle inequality arguments:
Proving the properties of limits: • How can we be sure of the limit properties...