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Programmer Mind vs Mathematician Mind (Humility)
In the past I thought so: Common money-earning programmers just have the skill to comprehend with their egg-heads how program flow moves between multiple levels of functions and classes calling each other in a “perverted”, unpredictable, messy fashion. While I am a programmer, too, I am different: I am a mathematician, I comprehend abstraction, generalization, […]
An infinitely big structure in the center of a black hole?
I remind that I defined generalized limit of arbitrary function. The limit may be an infinitely big value. It allows to define derivative and integral of an arbitrary function. I also defined what are solutions of partial differential equations where such infinities (instead of e.g. real numbers or complex numbers) are defined. You may see […]
New Edition of the Book “Algebraic General Topology. Book 1: Basics”
I’ve published a new edition of my book Algebraic General Topology. The new edition features “unfixed morphisms” a way to turn a category into a semigroup. (Certain additional structure on the category is needed.) The book features a wide generalization of general topology done in an algebraic way. Now we can operate on general topological […]
A Popular Introduction into the Generalized Limit (of arbitrary discontinuous function)
Abstract. A review of my book “Generalized limit (of arbitrary discontinuous function)”. A popular introduction with graphs to the following topic: I consider (a generalized) limit of an arbitrary (discontinuous) function, defined in terms of funcoids. The definition of the generalized limit makes it obvious to define such things as the derivative of an arbitrary […]
Generalized Limit Expressed through Ultralimits
In my book Limit of a Discontinuous Function I defined the generalized limit defined for every (even discontinuous) function. The definition of my generalized limit uses the concept of funcoids. Funcoids are a little advanced topic, what somehow hinder understanding of generalized limit by other mathematicians. But in the special case of a function p […]
What is Algebraic General Topology (Video)
Algebraic general topology – what is it? First, what is a general topology? General topology is the theory of topological spaces, as well as uniform spaces, proximity spaces, and metric spaces. I made a rather big discovery – a general theory that generalizes all these types of spaces in one algebra. That is, instead of […]
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.