## Number Sets and Integers

### 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.

e.g. {infinite, non-recurring decimals} • The set of real numbers (rational numbers + irrational numbers)

R = {all 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 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:

 ×/÷ +ve -ve +ve + - -ve - +

Examples:

 For multiplication For division 4 × 2 = 8 4 ÷ 2 = 2 - 4 × − 2 = 8 - 4 ÷ − 2 = 2 4 × − 2 = − 8 4 ÷ − 2 = − 2 - 4 × 2 = − 8 - 4 ÷ 2 = − 2