Youtor
Prove the Triangle Inequality Real Number Case
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=i3kO0uBxkew
Baby Rudin (Walter Rudin's Principles of Mathematical Analysis ): https://amzn.to/2sm99LF. Proof of the triangle inequality. Real Analysis Proofs Playlist: • Prove Square Roots of Non-Perfect Squ... . Amazon Prime Student 6-Month Trial: https://amzn.to/3iUKwdP. Check out my blog: https://infinityisreallybig.com • Real Analysis Proofs, Video #7 (Fundamental Inequalities V). Use the formula for the absolute value function and basic lemmas. It is best to structure the proof of the triangle inequality through the use of lemmas. • Introductory Real Analysis Lectures Playlist: • Introduction to Real Analysis Course,... • (0:00) Statement of the triangle inequality • (1:13) Define |x|, the absolute value of a real number, with a piecewise formula • (2:42) Lemma 1: -|a| is less than or equal to a is less than or equal to |a| • (3:34) Lemma 2: Inequalities are preserved by addition • (4:13) Lemma 3: |a| is less than or equal to c if and only if a is between -c and c • (5:22) Prove the triangle inequality using the lemmas • (9:16) Prove Lemma 1 using cases • (11:15) Prove Lemma 2 • (12:24) Prove Lemma 3 • AMAZON ASSOCIATE • As an Amazon Associate I earn from qualifying purchases.
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