lesson 5 Flashcards
are used to group objects together. Often, but not always, the objects in
a set have similar properties.
Sets
A set is an unordered collection of objects, called – or – of the set.
elements or members
A set is said to contain its elements. We write α ∈ A to denote that α is an element of the set A. The notation α ∉ A denotes that α is – of set A.
not an element
It is common for sets to be denoted using –
uppercase letters
Lowercase letters are usually used to – elements of sets.
denote
is where elements is presented by listing them inside of bracket.
Roster Method
are used when the general pattern of the elements is obvious.
Ellipses (…)
– is another way to describe a set. It is characterized by all elements in the set by stating the – or – a set may have to its members.
Set Former Notation, property or properties
what set is this N = 1,2,3,4, …
Set of Natural Numbers
What set is this W = 0,1,2,3,4, …
Set of whole Numbers
What set is this Z = … , −2, −1,0,1,2, …
the set of integers
what set is this Z+ = 1,2,3,
the set of positive integers
what set is this Z− = −1, −2, −3, …
the set of negative integers
what set is this what set is this Q =
p
q p ∈ Z, q ∈ Z, and q ≠ 0
the set of rational numbers
Two sets are equal if and only if they have the – .
same elements
A set with no elements is called the – represented as ∅.
empty (null) set
A set with 1 element is called a – while a set with two elements is
called an –.
singleton, unordered pair
The set A is a – of B if and only if every element of A is also an element of B.
subset
A is a – of B (A ⊂ B) because some elements from A are not present in B.
proper subset
Let S be a set. If there are exactly n distinct elements in S where n is a non-negative integer, we say that S is a finite set and that n is the – of S.
cardinality
The – or – of the set A, A , is the number of elements in the set.
size or cardinality
A set with limited number of set is called –, otherwise its called
–.
finite set, infinite set
Given a set S, the – of S is the set of all subsets of the set S.
power set
the empty set and the set itself are members of this set of –.
subsets
The – (a1, a2, … , an) is the ordered collection that has a1 as its first element, a2 as its second element, …, and an as its
nth element.
ordered n-tuple
two ordered n − tuples are equal if and only if each corresponding pair of their elements is –.
equal
