## 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

## 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

## 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

AGT isn’t new math that’s intended to replace existing mathematical theory, but rather a novel way to express mathematical concepts

## 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