Set Definition:
A collection of objects.Examples include letters, number, fruits.
Set Notation
{1, 2, 3, 4, 5}Use braces {} to enclose a set
Use 3 dots for infinity
{1, 2, 3, ...}
Use capital letters for sets
S = {1, 2, 3}
Examples of Sets:
Letters of the alphabet {a, b, c}Coins: {penny, nickel, dime}
Counting Numbers {1, 2, 3, ...}
Positive Even Numbers {2, 4, 6, ...}
Elements of sets:
Each element separated by commasElements use the element symbol ∈
In the set S = {1, 2, 3}
1 ∈ S, 2 ∈ S, 3 ∈ S
Cardinality of a set:
Measures how many elementsGiven a set S, cardinality = |S|
With S = {1, 2, 3}, |S| = 3
since S has 3 elements
Special Type of Sets:
The Universal Set U has every elementThe empty set ∅ has no elements
Complement of a set:
Everything not in the set but in UWrite this as S' or SC
Given U = {1, 2, 3, 4, 5} and S = {1, 2, 3}
SC = {4, 5} since they are in U not in S
Finite sets:
Finite sets have countable elements.{1, 2, 3} for example has 3 elements
Infinite sets:
Infinite sets have uncountable elementsThey go on forever using ...symbol
{1, 2, 3, ...}
Set Notes:
Element order does not matter{1, 2, 3} = {3, 2, 1}
How does the Sets Calculator work?
Free Sets Calculator - This lesson walks you through what a set is, how to write a set, elements of a set, types of sets, cardinality of a set, complement of a set.
What 5 formulas are used for the Sets Calculator?
Set is denoted with braces and commas separating elements {1, 2, 3}
Elements are members of items in a set S = {1, 2, 3}, 1 ∈ S
S = {1, 2, 3}, the cardinality |S| = 3 since S has 3 elements
The empty set ∅ contains no elements
Given a Universal Set U = {1, 2, 3, 4, 5} and S = {1, 2, 3} SC = {4, 5} since they are everything in the Universal set not in S
For more math formulas, check out our Formula Dossier
Elements are members of items in a set S = {1, 2, 3}, 1 ∈ S
S = {1, 2, 3}, the cardinality |S| = 3 since S has 3 elements
The empty set ∅ contains no elements
Given a Universal Set U = {1, 2, 3, 4, 5} and S = {1, 2, 3} SC = {4, 5} since they are everything in the Universal set not in S
For more math formulas, check out our Formula Dossier
What 11 concepts are covered in the Sets Calculator?
- cardinality
- a measure of the number of elements of the set
- coefficient
- a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
- difference
- the result of one of the important mathematical operations, which is obtained by subtracting two numbers
- element
- an element (or member) of a set is any one of the distinct objects that belong to that set. In chemistry, any substance that cannot be decomposed into simpler substances by ordinary chemical processes.
- index
- an indicator, sign, or measure of something
- intersection
- the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A.
A ∩ B - product
- The answer when two or more values are multiplied together
- set
- a collection of different things; a set contains elements or members, which can be mathematical objects of any kind
- sets
- subset
- A is a subset of B if all elements of the set A are elements of the set B
- union
- Combine the elements of two or more sets
Sets Calculator Video
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