We start with the **natural numbers**. These are the numbers
1, 2, 3, … (The … symbol means that the sequence goes on forever.)
They are used for counting. If we include zero then we get the
**whole numbers**, 0, 1, 2, 3, ….

The natural and whole numbers are usually considered to be exact (e.g. there are 4 tires on a car, 8 legs on a spider). But sometimes they are approximate (e.g. there were 1000 people in the crowd).

Here are the whole numbers, shown on the **number line**:

We say that 1 and −1 are opposites, 2 and −2 are opposites, etc. and we also say that −1 is the opposite of 1 and that 1 is the opposite of −1.

Negative numbers are used to describe debts as opposed to assets, temperatures below zero as opposed to temperatures above zero, heights below sea level as opposed to heights above sea level, and so on.

The set of numbers …, −3, −2, −1, 0, 1, 2, 3, … (the whole numbers and their opposites) is called the

Integer

Notice that if

Notice also that 3/1 = 3 and −5/1 = −5, so the rational numbers include all the integers.

Rational numbers can also be written in decimal notation instead of fraction notation. For example:

1/4 = 0.25The decimal notation 0.25 means literally “25/100” and 25/100 and 1/4 are equivalent fractions.

Notice that some rational numbers have no exact decimal equivalent. For example 1/3 is approximately equal to 33/100 but not exactly:

1/3 ≈ 0.33(The symbol ≈ means “

≈ 1.732,For this reason the Algebra Coach program will not convert irrational numbers to decimals when it is operating in exact mode.e≈ 2.718 and π ≈ 3.14,

The number line is useful for understanding

We use the symbol < to mean “

- 5 < 8 because 5 is to the left of 8.
- −5 < 2 because −5 is to the left of 2.
In fact any negative number is less than any positive number.
- 5 < 8 and 8 > 5 are two ways of stating the same fact.
- 3.14 < π < 3.15 I call this a “less than sandwich”.
It means that 3.14 < π and also π < 3.15. In other words the number
π is somewhere between 3.14 and 3.15.

Click here for more information on accuracy and significant figures.

- We started with the whole numbers (numbers like 3)
- We wanted opposites for these numbers so we created the integers (numbers like −3)
- We wanted to divide these numbers but needed the rationals to describe some of the results (numbers like 3/4)
- We wanted to take the square root of these numbers but needed the irrationals to describe some of the results (e.g. )

Where do imaginary and complex numbers go on the number line? The answer is they don’t. This picture shows the

The Algebra Coach program can run in real mode or complex mode. In real mode it will not carry out any operation that leads to a non-real number (such as taking the square root of a negative number).

Click here for more information on complex numbers.

If you found this page in a web search you won’t see the

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