Filters An Introduction

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

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

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

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

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.

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

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

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