Please fork the repository and submit a pull request, or just open an issue. Finish proofs that I am struggled with.Correct syntax and grammar, because I'm not a native English speaker.Still, my proofs could be wacky, non-rigorous, and incorrect.Īny helps are appreciated, especially for the followings: I do try my best to make every statement I wrote as correct as possible. (then automatically (m 1)/n ( m 1) / n will not be an upper bound. (Reference: Analysis 1, Terrence Tao, Exercise 5.5.2, page 121) Just choose the smallest m m for which m/n m / n is an upper bound. AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American. I use the default recipe to build main.tex. It is a step in the proof of existence of least upper bound. I use vscode extenstion latex-workshop to build PDF file from TeX. One has to install texlive before compiling tex files (official installation is recommended). So, many thanks to the people who provided their solutions at math.stackexchange,, and many other sources. Most exercises cannot be completed without referencing solutions from online forums. My notes cover statements I found important or interesting, including almost all axioms, corollaries, exercises, lemmata, proofs, propositions, remarks, and theories in both books.Įrrata on Tao's website ( Analysis-I and Analysis-II) are used to correct errors in both books. These are my notes on the books Analysis I and Analysis II, 4th edition, written by Terence Tao. Analysis II Third Edition Terence Tao, University of California, Los Angeles This is part two of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus.
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