An Introduction to Mathematics
- ISBN-10
- 1230437452
- ISBN-13
- 9781230437453
- Series
- An Introduction to Mathematics
- Pages
- 48
- Language
- English
- Published
- 2013-09
- Publisher
- Theclassics.Us
- Author
- A. N. Whitehead
Description
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1911 edition. Excerpt: ... CHAPTER XIV SEKIES No part of Mathematics suffers more from the triviality of its initial presentation to beginners than the great subject of series. Two minor examples of series, namely arithmetic and geometric series, are considered; these examples are important because they are the simplest examples of an important general theory. But the general ideas are never disclosed; and thus the examples, which exemplify nothing, are reduced to silly trivialities. The general mathematical idea of a series is that of a set of things ranged in order, that is, in sequence. This meaning is accurately represented in the common use of the term. Consider, for example, the series of English Prime Ministers during the nineteenth century, arranged in the order of their first tenure of that office within the century. The series commences with William Pitt, and ends with Lord Rosebery, who, appropriately enough, is the biographer of the first member. We might have considered other serial orders for the arrangement of these men; for example, according to their height or their weight. These other suggested orders strike us as trivial in connection with Prime Ministers, and would not naturally occur to the mind; but abstractedly they are just as good orders as any other. When one order among terms is very much more important or more obvious than other orders, it is often spoken of as the order of those terms. Thus the order of the integers would always be taken to mean their order as arranged in order of magnitude. But of course there is an indefinite number of other ways of arranging them. When the number of things considered is finite, the number of ways of arranging them in order is called the number of their permutations. The number of permutations of a...
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- 2018-08-05
- 226 pages
- Paperback
- Createspace Independent Publishing Platform
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- 2017-06-15
- 218 pages
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