Empty Set - Definitions
#ALG-2-4
Category
Description
An introduction to the empty set.
Course(s)
Mini-Lesson
085
x
Algebra
091
x
Definition(s)
093
x
Sub-category
095
2.3
097
1.1
Set Theory
100
x
ADN
E18
x
PHT
x
Sets
A set is a collection of objects, which are called elements or members of
the set. A set is well-defined if its contents can be clearly determined. In
other words, the contents can be clearly named or listed based on fact
and not opinion. Sets are generally named with capital letters.
Empty Set
The set that contains no elements is called the empty set or null set and is
symbolized by { } or Ø.
(Note {Ø} is not the empty set. It is the set containing the empty set,
which is different.)
Rule
Example
Familiarize yourself with the basic vocabulary for the empty sets.
What is contained in the empty set?
Absolutely nothing!
Zero, nor the empty set itself, are contained in the empty set.
Use notation for the empty set carefully!
Practice
Remember!
A set is a collection of objects.
Problems
True or False (If false explain why.):
1. ∅ = { }
2. ∅ = { 0 }
3. ∅ = { ∅ }
ALG-2-4 | Page 1
See also
Practice
ALG-2-1: set - definitions
Answers
True
False
The empty set does
not contain zero,
because it contains
nothing.
ALG-2-4 | Page 2
False
The empty set does
not contain the empty
set, because it
contains nothing.