Baby Rudin (Walter Rudin's "Principles of Mathematical Analysis"): [ Ссылка ]
Real Analysis Proofs Playlist: [ Ссылка ]
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Introductory Real Analysis Lectures Playlist: [ Ссылка ]
Real Analysis Proofs, Video #9 (Fundamental Inequalities VII). Use properties of dot (inner) products and the Cauchy-Schwarz inequality.
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Idea of Proof of Triangle Inequality on R^n
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complexanalysisreal analysistriangle inequalityinequalityless than or equal tovectortriplen-tuplen tupleEuclideandot productinner productnormmagnitudesquare rootsum of squarestrigonometrylaw of cosinestriangle inequality on r^ntriangle inequality in r^neuclidean normcauchy schwarz inequalitygeneralized triangle inequality prooffundamental inequalitiesPythagorean theoremcommutative lawdistributive lawuse cauchy schwarz inequality
