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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: SYMBOLIC ALGEBRA, The Algebra Of Algebraic Numbers. 1. It will conduce to a better appreciation of the subject if we first give very briefly the usual method of deducing the ground rules for arithmetical numbers and point out their limitations. We shall first then regard the letters used as symbols to denote ordinary numbers. 2. Addition.?Let it be required to add(8a-96) to (56-4a). It is tacitly assumed that (8a?9b) is positive and denotes a real number, also that (5b ?4a) is positive and denotes an ordinary arithmetical number, whole or fractional. That is, we assume that if the proper numerical values are substituted for a and b, that 8a is greater than 96, and that 5b is numerically greater than Now, if we simply add 5b to (8?96), we have (5 ] 8a?96), but this sum is too great by 4a, as we had to add 5b diminished by 4a, so that we must subtract 4z from this first result to get the correct sum, which is therefore, 56 + 8a?96?4. In order to reduce this expression to its fewest terms, we have to make use of the law, that is easily proved for numbers, that the order in which we combine the terms is immaterial. Thus, if from (56 + 8ffl) we subtract 96, the result is (8?46), since we evidently reach the same value by adding 5b to 8a and then subtracting 96, as in simply subtracting 46 from 8. From 8a?46, we have now to subtract 4a, giving 4a?46 for the correct answer. In practice we set down the terms and add thus: 8?96 ?4a + 56 4a-46 But it must be distinctly understood that ?4a by itself means nothing, andthat we have only written for convenience like terms under each other, so that (?4a + 56) must be interpreted (56?4a), which is agreeable to the law mentioned. From a consideration of such examples we deduce the law in addition: Combine lik...
| ISBN-13 | 9780217055673 |
|---|---|
| ISBN-10 | 0217055672 |
| Weight | 0.23 Pounds |
| Dimensions | 9.00 x 6.00 x 0.14 In |
| List Price | $14.14 |
| Format | Paperback |
|---|---|
| Pages | 60 pages |
| Publisher | |
| Published On | 2009-08-01 |
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