Principles of Mathematical Analysis |
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Page 19
Walter Rudin. Countable sets are sometimes called enumerable , or denumerable . For two finite sets A and B , we evidently have A ~ B if and only if A and B contain the same number of elements . For infinite sets , however , the idea of ...
Walter Rudin. Countable sets are sometimes called enumerable , or denumerable . For two finite sets A and B , we evidently have A ~ B if and only if A and B contain the same number of elements . For infinite sets , however , the idea of ...
Page 25
... finite number of points of E. Let q1 , ... , qn be those points of N n E ... finite set of positive numbers is clearly positive , so that r > 0 . The neighborhood N , ( p ) contains no ... set of all integers . ( ELEMENTS OF SET THEORY 25.
... finite number of points of E. Let q1 , ... , qn be those points of N n E ... finite set of positive numbers is clearly positive , so that r > 0 . The neighborhood N , ( p ) contains no ... set of all integers . ( ELEMENTS OF SET THEORY 25.
Page 33
... finite , there is nothing to prove . If K is infinite , let E be an infinite ... set of points z such that zx < 1. The collection { G } is an open covering of K. By the Heine - Borel theorem , there is a finite ... SET THEORY 33 Perfect sets.
... finite , there is nothing to prove . If K is infinite , let E be an infinite ... set of points z such that zx < 1. The collection { G } is an open covering of K. By the Heine - Borel theorem , there is a finite ... SET THEORY 33 Perfect sets.
Contents
Preface V | 1 |
Elements of Set Theory | 18 |
Numerical Sequences and Series | 36 |
Copyright | |
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B₂ bounded variation c₂ called Cauchy sequence Chap choose compact set complex numbers consider contains continuous function continuous on a,b converges uniformly Corollary countable set Definition denote derivative differentiable discontinuous diverges equations Example exists f be defined f is continuous f(x+ fn(x Fourier series function defined function f ƒ and g ƒ ɛ given Heine-Borel theorem Hence implies inequality integral interval Let f lim inf lim sup limit point mean value theorem metric space monotonic functions monotonically increasing neighborhood nonnegative notation obtain open set partial sums partition polynomials positive integer power series Proof prove rational number Riemann Riemann integrable say that ƒ series converges set of points set of real Suppose f uniform convergence vacuous variation on a,b write Zan converges zero