MATH MIDTERM REVIEWER

Set

refers to a group or collection of well-defined distinct objects

Set is represented by

upper cases A, B, C…..

Elements

objects that belong in a set

Elements are also know as

members of the set

Roster Method

Method of listing the elements inside a pair of braces. Commas are used to separate the elements.

Examples of natural numbers

N= (1,2,3,4,5)

Examples of whole numbers

W=(0,1,2,3,4,5,6)

Integers

Z− , Z+ = {..., -4,-3,-2,-1,0,1,2,3,4,...}

Rational Numbers

Q = the set of all terminating or repeating decimals

Real Numbers

R = the set of all rational or irrational numbers

Imaginary Numbers:

i = A number that when squared gives a negative result

Complex Numbers:

C = is a combination of a Real and Imaginary Number

C = 7 +3i

Whole Numbers

are the numbers without fractions and it is a collection of positive integers and zero

Natural Number

is an integer greater than 0 and thus, natural numbers begin at 1 and increment to infinity. Natural numbers are also called "counting numbers" because they are used for counting

Counting numbers

Natural Number

Integer

a whole number which can be either a negative, positive

and zero, and represented by symbol “Z+, Z− ”.

Rational Number

is a number that can be in the form p/q where p and q are integers and q is not equal to zero and represented by symbol “Q”.

Irrational Number

is a number that cannot be written as a ratio of two integers and represented by symbol “P or Q’ ”.

Real Numbers

are all the numbers on the Number Line and include all the Rational and Irrational Numbers and represented by symbol “R”.

Imaginary Number

simply when number is squared it gives a negative result

and represented by symbol “ i ”.

Complex Number

is a combination of a Real number and an Imaginary number and represented by symbol “ C ”.

Cardinality

defines the number of elements a set is having. It describes also the size of a set or simply the number of distinct elements in the set.

A set is well defined if?

determines whether any given item is an element of the set.

Statement Form (Descriptive Form)

is a well-defined description of the elements of the set is given and the same are enclosed in braces.

Roster Form (Tabular Form)

Listing the elements of a set inside a pair of braces { } and are separated by commas.

Set Builder Form (Rule Form)

indicates a rule, or formula or a statement which is written within the pair of braces so that the set is well defined.

Set builder form

all the elements of the set, must possess a single property to become the member of that set

Null Set (Empty Set)

a unique set which have no element in it.

Universal Set

the set of all elements

Universal set

All other sets are subsets of the universal set.

Finite Set

the process of counting of elements surely comes to an end.

Infinite Set

denoted by three dots.

Venn Diagram

“Euler-Venn diagram”

Venn diagram

a simple representation of sets by diagrams.

Relation

relationship between sets of values.

Relation

is a subset of the Cartesian product

Cartesian Product

multiplication of two sets to form the set of all ordered pairs.

René Descartes

invented the Cartesian product.

It must be present when a relationship exist

Two sets are involved.

It must be present when a relationship exist

There must be a clear rule describing the relationship.

It must be present when a relationship exist

There is a directional property, that is, the relation is defined from one

set called the domain on to another set called the codomain.

Representing Relations

Arrow Diagrams and Ordered Pairs

Arrow Diagram

often used to represent a relation.

Ordered Pair

preserves the directional property of the relation.

Ordered Pair

It is consistent with the order of points plotted on a Cartesian Plane represented

Binary relation