Set theory Flashcards
Set
A set is a collection of objects whose contents can be clearly determined
Elements
The objects in a set are called elements or members
Naming sets
Capital letters are generally used to name sets
Word description of a set
Describing a set using words telling what the conditions of being a member are
e.g. “set W is the set of days of the week”
Roster method
Listing the elements of a set inside a pair of braces { }
Set-builder notation
A specific way of representing a set
e.g.
W = {x | x is a day of the week}
Read as: Set W is the set of all elements x such that x is a day of the week.
The empty set
The empty set, also called the null set, is a set that contains no elements. The empty set is represented by { } or Ø.
∈
Symbol used to indicate that an object is an element of a set; read as “is an element of”
ex. a ∈ B
∉
Symbol used to indicate that something is not an element of a set; read as “is not an element of”
ex. a ∉ C
Set of natural numbers
The set of natural numbers is represented by the bold face letter N
Cardinal number/cardinality
The cardinal number or cardinality is the number of elements in a set.
Cardinality symbol
The cardinal number of set A, represented by n(A), is the number of distinct elements in set A. The symbol n(A) is read “n of A.”
Repeating elements in a set
Repeating elements in a set neither adds new elements to the set nor changes its cardinality
Equivalent sets
Sets that contain the same number of elements
One-to-one correspondence
Sets in which every one element from a set can be matched with exactly one element from another set
