The natural numbers

In this episode I look at the Natural Numbers; also known as the counting numbers they form the countable infinite set of whole numbers beginning with one...or sometimes zero. I briefly discuss their origins and why they are so important before I tell you what some of them...ok quite a few of them...are.

 

Transcript:

Hello listeners welcome to the first episode of the restful maths podcast the, podcast that aims to make maths restful not stressful. Today I thought I’d start with the natural numbers. The what now? What are natural numbers? Well the natural numbers are the numbers which occur most commonly in nature; they are also known as the counting numbers: the whole positive numbers: 1, 2, 3, 4,…in other words the first numbers you learned about.

What’s so special about the natural numbers I hear you ask. Well they are the set of numbers which forms the foundation of modern civilization. At some points in our diverse histories as human kind, all civilizations needed the ability to count things in order to develop; so the concept of counting things and the creation of formal counting systems which evolved into what we now call the natural numbers is an important step in human evolution. There is modern day evidence that in less developed civilizations, the restricted need to count meant the existence of a very limited formal counting system; this is often known as the “one, two, many” phenomenon. I’ll post a link to an interesting article on this in the show notes, but even where there is evidence of the existence of one, two, many, the concept of tallying, one of the most basic ways to count things still exists. And this is important because the to us simple ability to tally – the concept of oneness, twoness, threeness and so on - is an intellectual and philosophical keystone in the development of humanity.

Now I said at the beginning that the natural numbers are also known as the counting numbers, so traditionally they started with one. After all zero tends not to exist in nature and it is challenging to say the least to count something which doesn’t exist. In fact the whole concept of the number zero is a human invention which reflected different developmental needs around the world, but it is generally agreed that the concept of zero as we understand and use it today has its origins in India. I’ll put a couple of links to books about zero which are worth reading in the show notes.

So traditionally zero is not included in the natural numbers, but in some fields of maths such as set theory, it makes sense to include zero in the counting system and so it is sometimes added. But for the purpose of this podcast I’m going to stick to the counting definition and start with the number...

 

Links:

Is one, two, many a myth? 

The Nothing That Is (Link to Amazon)

Zero: the Biography of a Dangerous Idea (Link to Amazon)

Title music: Music box melody by xanadou at Freesound