Calculus: The Logical Extension of Arithmetic re-examines the calculus paradigm by expanding the set of âindeterminate formsâ espoused by lâHĂŽpital 320 years ago. Starting from the 54 possible binary combinations of the foundational numbers (zero, one and infinity), a replacement for the function theory formulated earlier by Newton and Leibniz, is presented. A logical extension of the three concepts of differentiation, integration and the Naperian base number e follows this introduction, which is interpreted as âzero divided by zeroâ, âinfinity times zeroâ and âone raised to the infinite powerâ, respectively. The concept that a number postulated as representing ânothingâ is reinforced a useful connection to calculus theory. This treatise proposes a âsimilarâ number to denote and quantify âallâ, in order to understand the concept of infinity. Other topics covered in this text include analytical geometry, infinite sequences and infinite series.
Calculus: The Logical Extension of Arithmetic is a useful reference on advanced calculus theory for mathematics students and researchers.