Infinitesimal Calculus on the Reverse in my Book “Limit of a Discontinuous Function”

Traditional calculus as first considered in 17th century by Isaac Newton (and Leibniz, however some say Leibniz stole the Newton’s idea) and then 150 years later formalized (formulated correctly) by Cauchy and Weierstrass, uses limits. Initially calculus was called “infinitesimal calculus”, but in recent time the collocation “infinitesimal calculus” is usually used for a more […]

Some Conjectures About Generalized Limits

Continuing my research from general topology monograph Algebraic General Topology, the following new open problems arose: I remind that I define generalized limit of arbitrary function. This limit is defined in terms of funcoids. As I show in the Book 3, Algebra, generalized limit is defined for generalized spaces, for example for reloids. So, how […]

Book “Axiomatic Theory of Formulas: Algebraic Theory of Formulas”

“Axiomatic Theory of Formulas: Algebraic Theory of Formulas”: Paperback E-book Homepage Mathematicians studied everything except formulas 🙂 Now there is an abstract axiomatic system for formulas, too. Read my book. For mathematicians, programmers, and students.

Every Pointfree Funcoid on a Semilattice is an Algebraic Structure

Continuing this blog post: The set of all pointfree funcoids on upper semilattices with least elements is exactly a certain algebraic structure defined by propositional formulas. Really just add the identities defining a pointfree funcoid to the identities of an upper semilattice with least element. I will list the exact list of identities defining a […]

Funcoid is a “Structure” in the Sense of Math Logic

A few seconds ago I realized that certain cases of pointfree funcoids can be described as a structure in the sense of mathematical logic, that is as a finite set of operations and relational symbols. Precisely, if a pointfree funcoid $latex f$ is defined on a lattice (or semilattice) with a least element $latex \bot$, […]

A Book for Mathematicians and Programmers – Axiomatic Theory of Formulas

Algebraic Theory of Formulas

A new book for mathematicians and programmers published: Axiomatic Theory of Formulas or Algebraic Theory of Formulas. The book is an undergraduate level but contains a new theory. Get it: PAPERBACK E-BOOK From the preface: This new mathematical theory developed by the book author researches the properties of mathematical formulas (aka expressions). Naturally this theory […]

Limit of Discontinuous Function

No root of -1? No limit of discontinuous function? Like as once roots were generalized for negative numbers, I succeeded to generalize limits for arbitrary discontinuous functions. The formula of limit of discontinuous function is based on algebraic general topology, my generalization of general topology in an algebraic way. The formula that defines limit of […]

The book “Algebraic General Topology” published officially

After a long time of being an unaccepted genius, the first volume of my book Algebraic General Topology is published officially (by the biggest Russian science publisher INFRA-M). The most general in general topology and algebraic theory, generalization of limit for multivalued discontinuous functions, algebraic formula of continuity (for multivalued functions), common theory of calculus […]