Types of Numbers

When you first learn to count, you are learning the natural numbers: 1, 2, 3, 4,...(N). These are also known as the positive integers (Z⁺). Later you add the concept of zero and negative numbers. All of these together form the integers (Z). The positive numbers together with zero are called the whole numbers (W).

As you grow older you learn about the concept of a fraction of a whole. At that point you are introduced to the rational numbers (Q).

At some point you learn about square roots such as . Then you realize that not all square roots can be written as a quotient of integers (); thus we have the concept of the reals (R).

Later still, you decide to take the square root of a negative number and the idea of an imaginary number is introduced: i º ). When you have a number with both a real and imaginary part added together, you have a complex number (C). 3 + 2i and ½ -3i are examples of complex numbers. Note: 5 is a complex number with an imaginary part of 0i.

More notation:

We say 5/2 Î Q (five halves is an element of the rationals)
R Í C (The reals are a subset of the complex numbers.)

For each number below identify which of the following categories they fit into.

The categories are:

integers: Z
rationals: Q (numbers that can be written as where a and b are integers and )
irrationals: R\ Q or I (a real number that cannot be written as rational number)
reals: R
pure imaginary: ( a complex number that does not have a real component: bi)
complex: C (can be written as a + bi where a and b are real numbers and i º )

1.) 5	2.) p	3.)
4.) 3.18	5.)	6.)
7.) 5 + 6i	8.)	9.)

Solutions: