This book introduces the reader to the author's theory of the arithmetic properties of a class of numerical functions, which is the first in an infinite sequence of such classes, which the author labels 'numerical functions'. These functions can be employed to describe many phenomena in arithmetic. The author sets out the development of this theory with the aim of showing that the postulates and processes of arithmetic admit of a multiplicity of interpretation. After developing the general theory, the author concludes by examining its properties and applications. Scholars with a background in arithmetic will find the novel perspective on the subject inspiring.
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Excerpt from An Arithmetical Theory of Certain Numerical Functions
T3.29. If e is a unit, 50 any functional form [general, as m at W AS in in each term except that for which d 1, vanishes; viz., the sum reduces to Wu). Hence, etc.
If in any equivalence, either of W W may replace the other (without affecting the validity of the equivalence), then W W are identically equivalent: symbolically it 2 W.
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