Summary - MAM1031F (MAM1031F)

,At :
Natural numbers [1 .
2 3
.
...
3

: Integers 2-2 .
-1
.
0
.
1
.
2 ...
3

⑫: Rational numbers [IR where b 03
: Real

Q :

Complex



Set Builder Notation

y
= & set with objects I rule3

eg. k = GoEIR/ocEN & 3 x 7753 x =
.




1x
Cardinality =




&
number of elements in a set


① =
empty set




Set : well-defined mathematical collection of distinct objects


The Union (U)
AUB = GolocEA or sEB

1 .
AUB =
BUA :.
Commutative

.
2 AU (BUC) = (AUB)UC :. Associative can reorder brackets)


The Intersection (1)
Al B =
ExloEA and of BY
1 . A 1B =
B1A : commutative

2AM (BMC) =
(AMB) 1C : Associative



The Set Difference (1)
AlB = B)A

AlB =
GxlocfA and xEB3

, in s is in set A
every element

Subsets (f)
A can = S
~
&
A set S is said to be a subset of a Set A (SEA) ,
it each element of S is an element of A
.




of A is in C but differing
Proper Subset (C) Every element C has at least one element



-Every element of set A is in set c and A C


&: not a subset




is subset for all sets
Empty set
always a




# c c QC IR



Intervals

C ,
0
,
< = not
including
C .0, including


Inequalities
I . 18 add and bCC : a C 4 . 18 a < b and C>0 :. ac LbC

.
2 18a(b : a + c >b + c 5.
5 18a < b and <O :. ac > be

.
3 Ifa < b and c (d : a + c b + d 6 .
18 09 < b :)


Proof that any function =
sum of odd and even function

g(x) f(x)
=
+ f) -

x)

n (x) = C(x) -
Gl -


x)


g(x) + h(x) = 2f(x)

Egx) + zh(x) =
f(x)

, Functions
A rule which maps you from elements of one set of elements to elements of another

8 :
A >
-


B
↓
For an element ofA there is a single element ScodEB



Domain :
the set of all values which the function can be applied to


Codomain : the set of all possible values that the function could take


Range
:
the set of all possible values that the function actually takes when applied to the elements

in the domain .




can be represented as 11) Words &I Formula 13/Graph (4) Table


Piecewise function
multiple pieces
function defined different intervals
by multiple sub-functions in
~
A .




I rule
Do each 11 as + 10



Gimme
1.
- G
eg So =
. .
2 Find the if .




3 . Find which equation fits
↑




function)
&



10 3 is not apart of 4
Simplify
30
.

.




10 0 is a part of the function
1z'
.



⑧ Not apart
· Apart



-

7
-
y = x
-




Absolute value function y
= x


-x)x(0)
(x) =
E I
-x)x20
eg .
(4) = 44 and 1-3) =
3