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General Arithmetic

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.
ID Code:6161
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:27 Nov 2006
Last Modified:14 Nov 2014 19:19

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