Virtual Calculus - Part I
Sergio Ferreira Cortizo
TL;DR
This paper introduces a new approach to differential and integral calculus using an extended real number system with infinitesimals and infinities, relying solely on elementary set theory.
Contribution
It presents a novel organization of calculus based on an extended real number system, avoiding complex logical methods.
Findings
Provides a consistent framework for calculus with infinitesimals
Simplifies calculus concepts using elementary set theory
Offers an alternative to traditional calculus methods
Abstract
An alternative organization for Differential and Integral Calculus, based on an extension of real numbers that include infinitesimal and infinite quantities, is presented. Only Elementary Set Theory is used, without reference to methods or results from Mathematical Logic.
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Taxonomy
TopicsMathematical and Theoretical Analysis