Numerical Sets
A set is a collection of objects that share a common structure or
property.
An element is an individual object that belongs to a set. They are
written in braces.
Sets are denoted by capital letters, and elements are written in
lowercase letters or numbers.
Example:
A = {a, b, c}
A — a set.
a, b, c — elements.
Elements can belong or not belong to a set.
Symbol:
∈ – Belonging
∉ —Non-belonging
Example:
A = {1, 8, 16, 70}
,1∈A
20 ∉ A
Types of Sets
• Finite set
• Infinite set
A finite set is a set whose elements can be counted. A finite set consists
of natural numbers.
A = {7, 8, 9, 10}
An infinite set is a set whose elements cannot be counted. An infinite set
consists of a range or interval.
A = [7; 10]
The set is infinite because:
7.1; 7.23; 8.5... To infinity.
• Empty Set
, An empty set is a set that contains no elements.
Symbol: ∅
• Subset
A subset is a part or group of elements that is completely contained
within another, larger set.
Symbol: ⊂
A = {1, 2, 6}
B = {1, 2, 3, 4, 5, 6, 7}
A⊂B
REMEMBER
For simplicity, let’s use two sets — A and B.
Set A is a subset of set B if all elements of set A also belong to set B.
However, if not all elements of set B belong to set A, then set B is not a
subset of set A.
A = {1, 2, 6}
B = {1, 2, 3, 4, 5, 6, 7}
B⊄A
A set is a collection of objects that share a common structure or
property.
An element is an individual object that belongs to a set. They are
written in braces.
Sets are denoted by capital letters, and elements are written in
lowercase letters or numbers.
Example:
A = {a, b, c}
A — a set.
a, b, c — elements.
Elements can belong or not belong to a set.
Symbol:
∈ – Belonging
∉ —Non-belonging
Example:
A = {1, 8, 16, 70}
,1∈A
20 ∉ A
Types of Sets
• Finite set
• Infinite set
A finite set is a set whose elements can be counted. A finite set consists
of natural numbers.
A = {7, 8, 9, 10}
An infinite set is a set whose elements cannot be counted. An infinite set
consists of a range or interval.
A = [7; 10]
The set is infinite because:
7.1; 7.23; 8.5... To infinity.
• Empty Set
, An empty set is a set that contains no elements.
Symbol: ∅
• Subset
A subset is a part or group of elements that is completely contained
within another, larger set.
Symbol: ⊂
A = {1, 2, 6}
B = {1, 2, 3, 4, 5, 6, 7}
A⊂B
REMEMBER
For simplicity, let’s use two sets — A and B.
Set A is a subset of set B if all elements of set A also belong to set B.
However, if not all elements of set B belong to set A, then set B is not a
subset of set A.
A = {1, 2, 6}
B = {1, 2, 3, 4, 5, 6, 7}
B⊄A
