1
Notes - Set Theory Introduction: Notation
Standardized Notations:

N


Z
 <

R


W
 =
 >

≥
≤
≠
Introductory Set Notation:


Definition of a set:
Braces

Set names:

Object, element or member:
N Butterworth,
Blackmon Road Middle School,
Columbus, GA
Rev August 2014
2
Roster Notation:

Definition of Roster Notation:

The seven dwarves:

Months in the school year:

All even integers:

All positive integers:

Integer multiples of 3:
The Elements of Set Builder Notation:

|

∈

∉
 ∅ 𝑜𝑟 { }
N Butterworth,
Blackmon Road Middle School,
Columbus, GA
Rev August 2014
3
Translating English Sentences (Descriptions) into Set Builder Notation:

The set of all s such that s is an element of the Natural Numbers and s is less than
or equal to negative twelve.

The set of all t such that t is an element of the Integers and t is greater than
negative seventeen.

The set of all m such that m is an element of the Real Numbers between negative
two hundred and fifty-three.

The set of all t such that t is an element of the Whole Numbers and t is between
twenty-one and eighty-four, inclusive.
Translating Set Builder Notation into English Sentences (Descriptions):

{𝑥|𝑥 ∈ 𝑅, 𝑥 ≤ 8}

{𝑚|𝑚 ∈ 𝑍, 𝑚 ≠ −42}

{ℎ|ℎ ∈ 𝑊, ℎ > 10}

{𝑔|𝑔 ∈ 𝑁, 47 < 𝑔 < 91}

{𝑦|𝑦 ∈ 𝑅, 𝑦 ∉ 𝑍}

{𝑘|𝑘 ∈ 𝑍, 𝑘 ∉ 𝑊}
N Butterworth,
Blackmon Road Middle School,
Columbus, GA
Rev August 2014
4
More Notation:

⋃
𝐴⋃𝐵

⋂
𝐴⋂𝐵

𝐴, 𝐴𝑐 , 𝐴′ this notation is not standardized, know all three.

𝑈

Definition of a subset:

⊆

⊂

⊄
N Butterworth,
Blackmon Road Middle School,
Columbus, GA
Rev August 2014