1. SETS & FUNCTIONS
NOTATION & TERMINOLOGY
SETS: A set is a collection of items which have some common property.
These items are called the members or elements of the set.
Sets can be described or listed using “curly bracket” notation.

2. eg {colours in traffic lights}
= {red, amber, green}
DESCRIPTION
LIST
eg {square nos. less than 30}
= { 0, 1, 4, 9, 16, 25}
NB: Each of the above sets is finite because we can list every member however the main sets of numbers are infinite.

3. Theses are
N = {natural numbers}
= {1, 2, 3, 4, ……….}
W = {whole numbers}
= {0, 1, 2, 3, ………..}
Z = {integers}
= {….-2, -1, 0, 1, 2, …..}
Q = {rational numbers}
This is the set of all numbers which can be written as fractions or ratios eg 5 = 5/ = -7/ = 6/10 = 3/ % = 55/100 = 11/20 etc

4. R = {real numbers}
This is all possible numbers. If we plotted values on a number line then each of the previous sets would leave gaps but the set of real numbers would give us a solid line.
We should also note that
N “fits inside” W W “fits inside” Z Z “fits inside” Q Q “fits inside” R

5. N Q W Z R
When one set can fit inside another we say that it is a subset of the other.
The members of R which are not inside Q are called irrational numbers. These cannot be expressed as fractions and include  , 2, 35 etc

6. To show that a particular element/number belongs to a particular set we use the symbol .
eg 3  W but  Z
Examples
{ x  W: x < 5 }
= { 0, 1, 2, 3, 4 }
{ x  Z: x  -6 }
= { -6, -5, -4, -3, -2, …….. }
{ x  R: x2 = -4 }
= { } or 
This set has no elements and is called the empty set.