Abstract
The various concepts of integral play a large party in the application of mathematical analysis to present-day science. This chapter examines the concept of Stieltjes integral. A denumerable set of denumerable sets is considered. The elements of all these sets can be denoted by a letter with two integral indices a(q)p. The upper index indicates the number of the set to which the element belongs, and the lower the number which the element has in the denumerable set to which it belongs. There is no difficulty in enumerating all the elements a(q)p. It is taken as the first element the one in which both indices are unity. The elements in which the sum of the indices is 3 is taken and arranged in order of increasing upper index. The elements in which the sum of the indices is 4 is taken and arranged in order of increasing upper index. This gives the fourth, fifth, and sixth elements of the sum of sets.
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