Ward, Morgan (1927) General Arithmetic. Proceedings of the National Academy of Sciences of the United States of America, 13 (11). pp. 748-749. ISSN 0027-8424 http://resolver.caltech.edu/CaltechAUTHORS:WARpnas27
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Abstract
The abstract theory of a mathematical system consisting of a set of elements and two operations "multiplication," and, later, "addition" is developed by postulational methods with examples. The more important results are the following. An "arithmetic" may be roughly described as a system in which 1. Every element is completely specified by a finite number of cardinal numbers. 2. "Division" is not always possible, and we can find when one element divides another element in a finite number of steps. 3. Unique re6lution into "prime factors" is always possible.
| Item Type: | Article |
|---|---|
| Additional Information: | Copyright © 1927 by the National Academy of Sciences Communicated October 15, 1927 |
| Record Number: | CaltechAUTHORS:WARpnas27 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:WARpnas27 |
| Alternative URL: | http://www.pnas.org/content/vol13/issue11/ |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| Metadata Review: | All Records > Caltech Library Services |
| ID Code: | 6161 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Archive Administrator |
| Deposited On: | 27 Nov 2006 |
| Last Modified: | 04 Jul 2008 20:42 |
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