What is a set with no elements called?
AnswerThe empty set
The empty set, written ∅ or {}, contains nothing at all.
Science · Facts & stats
Set facts & stats
7 fact-checked facts about sets in mathematics, each with the reason behind it. 5 more are in today's round and join this page after it closes.
The basics
Are the sets {1, 2, 3} and {3, 2, 1} equal?
AnswerYes, order does not matter in a set
A set is defined only by which elements it contains, not their order.
Going deeper
What does the symbol ∩ mean in set notation?
AnswerIntersection
A ∩ B contains only the elements that are in both A and B.
What does the symbol ∈ mean?
AnswerIs an element of
x ∈ A means that x belongs to the set A.
What is the number of elements in a set called?
AnswerIts cardinality
The cardinality of {a, b, c} is 3.
Expert level
Which mathematician founded set theory in the 1870s?
AnswerGeorg Cantor
Georg Cantor developed set theory and showed that some infinities are larger than others.
What is the power set of a set?
AnswerThe set of all its subsets
The power set of {a, b} is {∅, {a}, {b}, {a, b}}.
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