An Arithmetical Theory of Certain Numerical Functions (Classic Reprint) - Tapa blanda

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0.00. Apart from any evident utility as an economizer of thought and of calculation, there is, in the manifold interpretation of a system of postulates a wide philosophical significance.1 The numerous instances of this multiplicity of meaning that have been devised in geometry, are common knowledge; in arithmetic the comparatively fewer examples, among which the Theory of Ideals of Dedekind is the classic, do not seem to be so generally appreciated, possibly because they lie slightly to one side of the main progress of analysis, although, as asserted by some,2 arithmetic may be the proper foundation of all. The purpose of this paper is twofold; (i) To show, by several examples, that the postulates and processes of arithmetic admit of a multiplicity of interpretation, all examples to be simple and interconnected; (ii) To construct a self-contained arithmetical theory fcf. 0.01 (i)] of a large and important class of numerical functions, the theory to be so formed that the inter-relations

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