Posted on July 19, 2021July 19, 2021Complex Numbers are Real Complex Numbers are Beautiful Too Real Analysis Study Help for Baby Rudin, Part 1.7 Complex numbers can be represented either using Cartesian coordinates or polar coordinates. The geometric interpretation of complex multiplication is very beautiful using polar coordinates. Are imaginary numbers real? After all, why are they be called “imaginary”? Doesn’t this name imply that they don’t exist? To … Read the rest
Posted on June 14, 2021July 1, 2021Existence of nth Roots of Positive Reals The Completeness Axiom helps us prove the existence of nth roots of positive real numbers, but the proof is quite challenging. Real Analysis Study Help for Baby Rudin, Part 1.6 Ultimately, the continuity of at allows us to prove the existence of . Later, the argument is based on the Intermediate Value Theorem. In this article, the argument is … Read the rest
Posted on January 7, 2021January 24, 2021Baby Rudin: Let Me Help You Understand It! The First in a Series of Blog Posts on Baby Rudin Study Help for Baby Rudin, Part 1.1 My personal copy of Baby Rudin (Principles of Mathematical Analysis, 3rd edition, by Walter Rudin) The textbook “Principles of Mathematical Analysis”, by Walter Rudin, is considered a “classic” text on real analysis, the subject that uses rigorous deductive … Read the rest