W. Rudin  Principles of Mathematical Analysis

Название: 
Principles of Mathematical Analysis 
Автор: 
W. Rudin 
Категория: 
Математика

Тип: 
Книга 
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04.01.2009 11:49:34 
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Описание: 
A satisfactory discussion of the main concepts of analysis (such as convergence, continuity, differentiation, and integration) must be based on an accurately defined number concept. We shall not, however, enter into any discussion of the axioms that govern the arithmetic of the integers, but assume familiarity with the rational numbers (i.e., the numbers of the form m/n, where m and n are integers and n Ф 0).
The rational number system is inadequate for many purposes, both as a field and as an ordered set. (These terms will be defined in Sees. 1.6 and 1.12.) For instance, there is no rational p such that p2 = 2. (We shall prove this presently.) This leads to the introduction of socalled "irrational numbers" which are often written as infinite decimal expansions and are considered to be "approximated" by the corresponding finite decimals. Thus the sequence 
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