Computational Calculus

This book aims to computerize the concept of number.
The computer has always been a machine of approximate calculus; hence one may wonder when can a step forward to exact calculus be taken. The purpose of this work is to answer that question.

We accepted the challenge of creating Abstraction of Number and therefore carry out exact calculus. Throughout the pages of this book we introduce a model, a method and an algorithm to meet that goal. Our premise has been that Abstraction of Number is the theory that enables to computerize the concept of number, i.e. becoming it accessible to a computer.

In the approximate calculus context, the computer is seen as a machine that crunches the values of numbers, whereas within the exact calculus, a computer becomes an intelligent handler of numeric structures. Exact calculus is intelligent calculus. As calculus evolves, numbers seem like living entities, going through transformations and metamorphosis until reaching their final form. This is how one feels the intelligence of programs.

In the conclusion we make the study on numbers more comprehensive to create Abstraction of Function (real function of real variables). We are aware that the scientific community is not very receptive to this project. Thus, it is with intensified joy that we make the present work available to the public in general. The readers will have the last word: will they perceive Abstraction of Number as the solution to implement exact calculus? We look forward to know their opinion.