Lesson 157
Objective: Describe a set including the empty set.
Empty Sets
In set theory, the empty set is the unique set having no elements. The symbol for the
empty set is shown below.
Intersection of Sets
Intersection of two sets A ∩ B
The intersection (denoted as ∩) of two sets A and B is the set that contains all elements
of A that also belong to B (or equivalently, all elements of B that also belong to A), but
no other elements.
For example: The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
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Unions
In set theory, the union (denoted as ∪) of a collection of sets is the set of all distinct
elements in the collection.
For example: A = {1,2,3,4} B = {5,6,7,8} A ∪ B = {1,2,3,4,5,6,7,8}
Union of two sets: A ∪ B
Finite Sets
In mathematics, a finite set is a set that has a finite number of elements.
Infinite Sets
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable
or uncountable.
Some examples are:
The set of all integers, {..., -1, 0, 1, 2, ...}, is a countable infinite set.
The set of all real numbers is an uncountable infinite set.
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