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.
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 […]
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 […]
A Book for Mathematicians and Programmers – Axiomatic 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 […]
I am a genius that is all the rest are idiots (an article with too simple math formulas)
I made several scientific discoveries (mainly in abstract mathematics but also in XML files processing). I claim to be a genius based on this fact. But what I mean saying “I am a genius”? I mean just that all the rest experts showed themselves… idiots. Most of the formulas are too simple. Nobody guessed, nobody […]
A new easy theorem in my draft
A new easy theorem in my draft. Theorem $latex \mathrm{DOM} (g \circ f) \supseteq \mathrm{DOM} f$, $latex \mathrm{IM} (g \circ f) \supseteq \mathrm{IM} g$, $latex \mathrm{Dom} (g \circ f) \supseteq \mathrm{Dom} f$, $latex \mathrm{Im} (g \circ f) \supseteq \mathrm{Im} g$ for every composable morphisms $latex f$, $latex g$ of a category with restricted identities. Proof […]