The Set of integers Remember: The set of natural number N = {0, 1, 2, 3, ……… } The set of Counting number C = { 1, 2, 3, ……… } The set of integers Z = { …, -3, -2, -1, 0, 1, 2, 3 … } The set of positive integers Z + = { 1, 2, 3, …… } The set of negative integers Z - = { 1, 2, 3, …… }

Positive number : a number greater than zero

Negative number : a number less than zero

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level

Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction

Remarks: Z = Z + { 0 } Z - N Z Z + Z Z - Z Z Z-Z- Z+Z+ {0} N

We can use a Venn Diagram to represent the set of integers Z-Z- Z+Z+ {0} Z

10 In Summary Natural

The absolute value of an integer a = = The positive value of a For example: = 3 = 7 = 0

Express each of the following sets using the listing method: a)The set of integers less than 4 = { 3, 2, 1, 0, -1, ……… } b) The set of integers greater than -3 = { -2, -1, 0, 1, 2, ……… } c) The set of integers between -5 and 2 { -4, -3, -2, -1, 0, 1 }

d) The set of non-negative integers = { 0, 1, 2, 3, 4, ………….. } e) The set of non-positive integers = { 0, -1, -2, -3, -4, ………….. } f) The set of even positive integers = { 2, 4, 6, 8, ………… }

Put a) l -3l Z - b) -2 N c) {-5} Z d) N Z e) – l-7l Z - f) Z - Z g) Z + N h) Z N Put a) l -3l Z - b) -2 N c) {-5} Z d) N Z e) – l-7l Z - f) Z - Z g) Z + N h) Z N

Find the value of x in each of the following: l x l = 8 x = -8 or 8 l -2 l = x x = 2 -3 {-1, 3, x, -2 } x = -3 X { 4, 3, -2 } { -4, -3, -2 } x = -2 { 5, x } { -2, 0, 2} = { 5, -2, -5, 0, 2 } x = -5 l x l = 8 x = -8 or 8 l -2 l = x x = 2 -3 {-1, 3, x, -2 } x = -3 X { 4, 3, -2 } { -4, -3, -2 } x = -2 { 5, x } { -2, 0, 2} = { 5, -2, -5, 0, 2 } x = -5

Complete: … is the smallest positive integer. Sea level represented by the number … … is the greatest negative integer. The complement of Z - with respect to Z = …. The complement of N with respect to Z = … The complement of Z - with respect to Z - = …. The absolute value of -567 is …. … is the smallest positive integer. Sea level represented by the number … … is the greatest negative integer. The complement of Z - with respect to Z = …. The complement of N with respect to Z = … The complement of Z - with respect to Z - = …. The absolute value of -567 is …. 1 0 N Z-Z- { } 567

Put >, < or = l -4 l l -15 l l -4 l l -15 l

Complete: is the smallest positive integer. Sea level represented by the number is the greatest negative integer. The complement of Z - with respect to Z = The complement of N with respect to Z = The complement of Z - with respect to Z - = The absolute value of -567 is is the smallest positive integer. Sea level represented by the number is the greatest negative integer. The complement of Z - with respect to Z = The complement of N with respect to Z = The complement of Z - with respect to Z - = The absolute value of -567 is 1 0 N Z-Z- { } 567

19 Positive numbers move to the right Negative numbers move to the left (-8) = -5 Positive numbers move to the right Negative numbers move to the left (-8) = -5

Ordering and Comparing Integers (1)Arrange the following integers ascendingly: 3, -12, 5, -7, 1 The order: -12, -7, 1, 3, 5

(2) Arrange the following integers descendingly: 8, - 54, 9, - 22, 0, - 35 The order: 9, 8, 0, -22, -35, -54

(3) put >, < or = a)5 -7 b) c)I -14 l 4 d) I -2 l 2 e)5 + I -5 l 0 f) > < > > < =

(4) Write the previous integer and the next integer for each of the following integers: a) 19 b) -15 c) o Solution a)18, 20 b)- 16, -14 c) -1, 1

(5) Write the integers between each two integers of the following: a)-4, 3 b)-5, 1 Solution a)-3, -2, -1, 0, 1, 2 b) -4, -3, -2, -1, 0