Infinitesimal Calculus on the Reverse in my Book “Limit of a Discontinuous...
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...
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The Shortcomings of Topological Theory: The Reasons Why Generalized Algebraic...
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...
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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:
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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...
View ArticleGeneralized 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....
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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...
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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...
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The Potential Role of AGT in Economic Analysis
One of the fields of human inquiry that make extensive use of mathematics and calculus is economics. Contemporary economic theory relies heavily on mathematical concepts and ideas to make sense or and...
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Mathematical Research Reports: a “new” mathematics journal is launched
Gowers's Weblog From time to time academic journals undergo an interesting process of fission. Typically as a result of some serious dissatisfaction, the editorial board resigns en masse to set up a...
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