General Arithmetic

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.

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