2018년 7월 30일 월요일
0.Prologue
The purpose of this introductory chapter is to establish and remind elementary analysis and set theory which are backgrounds for Real Analysis.
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0.7 The Extended Real Number System
We briefly talk about materials in elementary real analysis. We will not prove those properties (see elementary real analysis textbook such ...
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Now we discuss fundamental axiom of set theory - Axiom of Choice. The following are equivalent. (The Hausdorff Maximal Principle). Eve...
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Now we move on to cardinality of sets. If $X$ and $Y$ are nonempty sets, we define the expressions $\left| X \right| \leq \left| Y \righ...
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Here, we define orderings (which are types of relations also) and fundamental theorems (Transfinite Induction and Bourbaki's Fixed Point...