Divisibility is a fundamental concept in mathematics, seamlessly integrated into our daily experiences, such as dividing a cake into equal parts or determining if one number is a factor of another. Traditionally, we understand divisibility to mean that a number \(a\) divides another number \(b\) (notated as \(a | b)\) if there exists an integer… Continue reading The Ideal Understanding of Divisibility

# Tag: algebra

## Horology, Slide Rules and Logarithms

Mathematics is obviously one of my interests, but admiring wrist watches is another. There’s something beautiful about the way a mechanical, battery-less contraption built up from miniscule parts could keep time as long as the wearer stays alive (of course taking into account servicing, etc but I digress). Placing a tool such as a watch… Continue reading Horology, Slide Rules and Logarithms

## Thoughts About Some Mathematical Practices

Here are some of my thoughts about some miscellaneous mathematical practices – some words of advice, warning, interesting insights, contentious disagreements, or whatever else comes to mind. This might become a multipart series as more comments come to mind in the future… Notation of Domains of Functions The domain of a function is a set.… Continue reading Thoughts About Some Mathematical Practices

## What Are Numbers? Pt. 4: The Real Numbers

This is the final part on a series on ‘What Are Numbers?’. In this part, we discuss the construction of the set of the real numbers. Part 1: The Natural Numbers Part 2: The Integers Part 3: The Rational Numbers Part 4: The Real Numbers Polynomial Equations In the previous parts, we constructed the Integers… Continue reading What Are Numbers? Pt. 4: The Real Numbers

## What Are Numbers? Pt. 3: The Rational Numbers

Welcome to a four part series on ‘What Are Numbers?’. In the previous part, we constructed the Integers by using the equivalence classes of Natural Number ordered pairs that represent equations in the form \(x + b = a\). For example, the Integer we write down in the usual way as \(-2\) describes the set… Continue reading What Are Numbers? Pt. 3: The Rational Numbers

## What Are Numbers? Pt. 2: The Integers

In Part 1, we see that the building blocks of numbers start with the Natural Numbers defined through the five Peano Axioms. In this post, we ponder the invention of the Integers. Welcome to a 4 part series (this is part 2) of ‘What Are Numbers?’. Part 1: The Natural Numbers Part 2: The Integers… Continue reading What Are Numbers? Pt. 2: The Integers

## What Are Numbers? Pt. 1: The Natural Numbers

In the last few days in the recent Covid Sydney lockdown period, I had a chance to read and revise on some abstract Algebra concepts such Group Theory, Rings, Fields and Galois Theory. I was reading mainly from the book “Abstract Algebra and Solution by Radicals” by John E. Maxfield and Margaret W. Maxfield amongst… Continue reading What Are Numbers? Pt. 1: The Natural Numbers