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.

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.

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 = 5/1 -7 = -7/1 0.6 = 6/10 = 3/5 55% = 55/100 = 11/20 etc

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

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

To show that a particular element/number belongs to a particular set we use the symbol . eg 3  W but 0.9  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.