TRIANGLE INEQUALITY for Absolute Value: INTUITION and proof!

A fun, accessible and comprehensive overview of the triangle inequality for the absolute value on the number line: what it is intuitively and in very simple examples, what it is mathematically, and how to prove it mathematically. The triangle inequality is one of the most important theorems/concepts in mathematics and regularly appears in problem solving in precalculus, calculus and all levels of advanced high school math, college math and beyond (including in homework, assignments, tests and exams). In this math tutorial, you will master the triangle inequality once and for all at the level of a professional mathematician! We will: Intuitively explain the triangle inequality for the absolute value in a way that makes it obvious Connect it to the moral lesson: "The journey is what matters, not the destination" State the triangle inequality mathematically and unpack it in words and simple examples Explain exactly when the triangle inequality is actually an equality/equation Give a mathematical proof of the triangle inequality completely rigorously and explain the thought process in detail Check out my playlist on the absolute value, my playlist on precalculus, and my playlist on proofs!    • The Absolute Value with Amitesh!      • Precalculus with Amitesh!      • Proofs with Amitesh!   If you enjoy the video, I would love if you could please like ✅ and subscribe 🎉, it means means so much to help support me in my goal of creating free and accessible math education worldwide! 😊