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

# Tag: proof

## 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

## The Language of Proof in HSC

Related Content Outcome MEX-P1 The Nature of Proof This post will primarily look at the following dot-point from page 28 of the Extension II syllabus: use the formal language of proof, including the terms statement, implication, converse, negation and contrapositive (ACMSM024) – use the symbols for implication (⇒), equivalence (⇔) and equality (=) , demonstrating a clear understanding of the… Continue reading The Language of Proof in HSC