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商品描述
This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.
商品描述(中文翻譯)
這段文字提供了實分析的基本概念和技術，適合所有這些領域的學生。它幫助學生培養演繹思考的能力，分析數學情境並將想法擴展到新的背景。與前三版一樣，本版保持了相同的精神和使用者友好的方法，增加了範例並擴展了邏輯運算和集合論的內容。此外，以下領域的內容也進行了修訂：在討論連續性之前介紹點集拓撲，對 limsup 和 liminf 進行更徹底的討論，直接在序列之後涵蓋級數，增加對 Lebesgue 積分及實數構造的介紹，並在可能的情況下引起學生對潛在應用的注意。
