Sets
Although set theory and operations are not now included in this course it is useful to know what a set is, and about the various number sets.
Notation
A set is a collection of objects. These objects, called the members or elements of the set, are enclosed in braces {...} and separated by commas.
A set can be described in words: A = { the first three natural numbers}
or by listing each member: A = {1, 2, 3}
Number sets
The numbers we use can be chosen from several sets.
 The set of natural numbers.

N = {1, 2, 3, 4, ...}

The set of whole numbers.
W = {0, 1, 2, 3, ...}

The set of integers.
I = {... 2, 1, 0, 1, 2, 3,...}

The set of rational numbers
Q =
e.g.

The set of irrational numbers
Irrational numbers are numbers that cannot be written as rational numbers.

The set of real numbers (rational numbers + irrational numbers)
Number lines
The number sets can be shown on number lines.
Natural numbers, N (excludes zero) Whole numbers, W (includes zero) Integers, I (positive and negative whole numbers) Rational numbers (all except irrationals) Real numbers, R (all numbers) 
Integers
The integers are the positive and negative numbers and zero.
For practice with integer calculations
Addition
Use a number line when adding and subtracting integers. The first integer is the starting point on the number line.
 When adding a positive integer, move to the right.
e.g. 4 + 2 = 6

When adding a negative integer, move to the left.
e.g. 4 + − 2 = 2
Subtraction
 When subtracting a positive integer, move to the left.
e.g. 4 − 2 = 2
 When subtracting a negative integer, move to the right
e.g. 4 − − 2 = 6
Multiplication and division
The rule is the same for both multiplying and dividing two integers.
If the signs of the two integers are the same, the answer is positive. If the signs of the two integers are different, the answer is negative.The table illustrates these rules:
Examples: