Calculus: The Logical Extension of Arithmetic re-examines the calculus paradigm by expanding the set of âindeterminate formsâ espoused by lâHĂ´pital 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.