Understanding Continuity from the Perspective of AGT
Continuity and limits, as understood in traditional calculus, rely on infinitesimally small sets to arrive at limits for arbitrary functions. This idea, when translated into other definitions of continuities, relies on ideas about convergence of sequences and the like.
What Is The Axiomatic Theory Of Formulas?
The methods or syntax to express mathematical truths are, obviously, essential to the study of mathematics. Without a taxonomy that highlights the correct use of mathematical symbols, rules which dictate the validity of mathematical statements and theory about how these statements are to be construed, you can’t do math.
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 […]
An Introduction to Filters—What’s So Special About This Partially Ordered Set?
AGT isn’t new math that’s intended to replace existing mathematical theory, but rather a novel way to express mathematical concepts which were previously inexpressible. I indulge these ideas because I believe, as is the modus operandi for all academics, that any worthwhile, logically consistent idea must be pursued until it is falsified or verified for […]
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 […]
Algebraic General Topology – A Game Changing Mathematical Theory
This new research field generalizes new theorems as well as former analysis by collapsing several theorems of analysis into one AGT equation:
The Shortcomings of Topological Theory: The Reasons Why Generalized Algebraic Point-Set Topology Is Superior
I feel that when the various fields of intellectual endeavor become obsessed with upholding tradition, they stifle room for original thought. The assumption that existing knowledge is complete and only linear, logical processes are worthy of examination, eliminates discourse buries novel, equally as valid ideas into obscurity. This absence of self-reflection is holding back new […]
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 […]