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Proof: Reverse Triangle Inequality Theorem | Real Analysis

The reverse triangle inequality tells us how the absolute value of the difference of two real numbers relates to the absolute value of the difference of their absolute values. In particular, |x-y| is greater than or equal to | |x| - |y| |. We'll prove this result in today's lesson. We'll need the normal triangle inequality theorem and another useful result about absolute value inequalities to prove today's result. Real Analysis Playlist:    • Real Analysis   Proof of the triangle inequality theorem:    • Proof: Triangle Inequality Theorem | ...   Proof of the absolute value inequality result we use:    • Proof: A Useful Absolute Value Inequa...   Thanks to Nasser Alhouti, Robert Rennie, Barbara Sharrock, and Lyndon for their generous support on Patreon! ◆ Donate on PayPal: https://www.paypal.me/wrathofmath ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   I hope you find this video helpful, and be sure to ask any questions down in the comments! +WRATH OF MATH+ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / @emery3050