## Monday, 14 July 2014

### Types of Numbers - The Number Line

There are so many different types of numbers with amazing properties that make them just beautiful, but I wouldn't be able to talk about these numbers without the most basic of numbers. So I am going to talk through the different numbers that make up the number line. (I said number a lot in that paragraph didn't I?)

First of all, we have the natural numbers or counting numbers. These are, as the name suggests, the numbers used to count things: 0, 1, 2, 3, 4, 5...

Next, we have the integers. These are the negative whole numbers along with the natural numbers: ...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...

Next are the rational numbers. These are numbers that are quotients of integers. In other words, numbers of the form a/b, where a and b are integers. There is an additional restriction where b cannot equal 0, since dividing by 0 causes all sorts of problems! Basically, rational numbers are just fractions: 1/2, 37/90, 3/4, -4/2 etc.

Next are the real numbers. These are the rational numbers along with numbers called the irrationals. These are numbers that cannot be written as a quotient of integers. They are numbers where the decimals don't terminate or repeat (in other words they go on forever without repeating). Any number that isn't rational is irrational. The most famous examples are: pi, e, the golden ratio and the square root of 2.

So these are the numbers that make up the number line. However, these numbers are not sufficient to be able to solve every equation. But more on that next time!