Cambridge International Mathematics

60 Sets (Chapter 2)

There are some number sets we refer to frequently and so we give them special symbols. We use:

²

² Zto represent the set of allintegers f 0 ,§ 1 ,§ 2 ,§ 3 ,§ 4 ,§ 5 ,§ 6 ......g

² Z+to represent the set of allpositive integers f 1 , 2 , 3 , 4 , 5 , 6 ......g

² Q to represent the set of allrational numberswhich have the form

p

q

wherepandqare integers and q 6 =0.

² R to represent the set of allreal numbers, which are numbers which can be placed on a number line.

Example 1 Self Tutor

True or false? Give reasons for your answers.

a 22 Z b 2212 Q c 52 =Q d ¼ 2 Q e ¡ 22 =R

a 22 Z is true

b 2122 Q is true as 212 =^52 where 5 and 2 are integers.

c 52 =Q is false as 5=^51 where 5 and 1 are integers.

d ¼ 2 Q is false as¼is a known irrational number.

e ¡ 22 =R is false as¡ 2 can be put on the number line.

Example 2 Self Tutor

Show that 0 : 36 , which is 0 : 36363636 ::::, is a rational number.

Let x=0:36 = 0: 36363636 ::::

) 100 x=36: 363636 ::::=36+x

) 99 x=36 and so x=^3699 = 114

So, 0 : 36 is actually the rational number 114.

B SPECIAL NUMBER SETS [9.2]

-2 -1 0 1 2 3 4 5 6 7 8 9 10

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-2 -1 0 1 2 3 4 5 6 78910

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

N to represent the set of allnaturalorcountingnumbers f 0 , 1 , 2 , 3 , 4 , 5 , 6 ......g

The set of natural numbers is endless, so we say n(N) is infinite.

as Z=f 0 ,§ 1 ,§ 2 ,§ 3 , ......g

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Y:\HAESE\IGCSE01\IG01_02\060IGCSE01_02.CDR Monday, 15 September 2008 12:05:26 PM PETER