We apply filters to existing sets to express otherwise inexpressible statements.They effectively allow us to refer to infinitely small or

Continue reading## Continuity as Convergence of Sequences—Expanding Our Definition of Continuity

I feel that continuity is best understood when we consider convergence at different levels of abstraction. While it’s fairly easy

Continue reading## 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

Continue reading## Understanding Functional Discontinuities – The Building Blocks Of AGT

A discontinuity is any point on a function where one of the three possibilities arise: The right-side limit is unequal

Continue reading## 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.

Continue reading## 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

Continue reading## 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

Continue reading## 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

Continue reading## 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

Continue reading## 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

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