Numbers - an Introduction

Numbers are just numbers . . . aren't they? Well, unfortunately it's a bit more complicated than that. It turns out that there are many different types of numbers. In fact, the same number can belong to many different sets of numbers. Numbers are a bit like people in that respect. A person can be a member of a particular profession (e.g. teacher, train driver, rocket scientist), be of a particular nationality (e.g. British, Chinese, French) as well as having a particular blood group (e.g. A RhD positive, B RhD negative, O RhD negative). And, just as every individual person on the planet is unique, so is every number you could possibly conceive of. I suppose the main difference between people and numbers is that numbers don't complain when you stick a label on them.

The way we look at a particular number very much depends on the way in which we want to use it. Suppose we invite a hundred people to attend a political meeting at the local town hall, and ask them to sign a register as soon they arrive. Once the meeting has commenced, we can check the register to determine how many people are actually in attendance. That way, if a fire breaks out, we can make sure that all those present have been evacuated by performing a head count. Alternatively, we can use the information to determine how many of the people invited were actually interested enough (in whatever issue was being discussed) to come to the meeting. Since we (rather conveniently) invited a hundred people, the number in attendance represents that information as a percentage.

You will of course already have encountered many different types of number in everyday life, perhaps without giving them much thought. Odd and even house numbers, for example, are (almost) always on opposite sides of the street. We often talk about time intervals using fractional values ("I'll be there in three-quarters of an hour . . ."). Statistics are of course quoted in newspaper and television reports with monotonous regularity. According to the UK Office for National Statistics, the average number of dependent children per married couple in the United Kingdom in 2012 was one-point-eight (1.8) children. When you actually think about statistics like this, you begin to realise that there is no such thing as the "average family". I certainly don't know any married couples with exactly one-point-eight children. Indeed, someone once said (probably either Mark Twain or Benjamin Disraeli) "There are three kinds of lies: lies, damned lies, and statistics."

Anyway, hopefully you get the point. Numbers are grouped into types depending on how they are represented, what kind of information they convey, and whether they have any special significance in a given context. We have whole numbers and fractional numbers, cardinal numbers and ordinal numbers, rational numbers and irrational numbers, real numbers and imaginary numbers, prime numbers, polygonal numbers (numbers that represent regular polygons), natural numbers - the list is almost endless. If you have an active imagination, the names given to some of these number types can conjure up strange images. Are irrational numbers, for example, prone to having friends that other numbers cannot see? (I refer of course to imaginary numbers). On a more serious note, you should become familiar with the various number types, and have some idea of how they are used. Whether studying mathematics for its own sake, or simply in order to underpin your studies in another field, you will inevitably encounter many of these number types and be expected to know what they mean.