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Iterated Limits in General Analysis

Iterated Limits in General Analysis


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1914. Excerpt: ... CHAPTER III. A Theory Of Functions Based On Properties Of A System (5)3; ll; T). 8. Introductory. In this chapter we are concerned with a definite system (5)5; U; T), which is assumed to satisfy the five postulates of 5. In 10 and 12, in order to provide for the features of iterated limits, special hypotheses are made with regard to the composite character of the system. Subclasses of 5)3 are, in general, denoted by 9t; but a definite one of these subclasses, denoted by 5)3, receives special consideration, being the range of the independent variable in our theory of functions. The derived class of $ is denoted by 2, and l is the least common superclass of 5)3 and 2. The letters p, q and I denote elements of the respective classes ty, D and 2, while a general element of 5)3 is written p, and q is an element of the class Q-$ + U. Functions are denoted by the letters 8, (i, etc. The notion of function, in general, involves two classes, one called the range and the other the class to which the function-values belong. If 3 and 3) are two classes of elements, then a function 6 on 3 to?) is a correspondence between elements of 26 and subclasses of?), whereby to every element x of 26 there corresponds uniquely a subclass 6X of 3). If, for every x, 9X consists of a single element y of 2), then 0 is a single-valued function on 36 to?). In the present chapter we consider only single-valued functions on a subclass of Q to 21, where 21 is the class of all real numbers with the ideal elements + and--co adjoined. The notation 21 stands for the class of all real numbers, and the letter a invariably represents a real number, while the letters e and d always denote positive real numbers. 9. The Character of a Function in ...


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Product Details
  • ISBN-13: 9781235675843
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 22
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 123567584X
  • Publisher Date: 01 Feb 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 59 gr

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