
What is the cardinality of a set?

If a set is finite (countable amount of elements), then the cardinality of A, $A$, is the number of distinct elements in A. The number of elements in set A can also be written as n(A).
Examples
Set

Cardinatlity

$$
A = \{2,4,6,8\}
$$

A =
4

$$
S=\{20,13,0,5\}
$$

S =
4

$$M=\{15,15,15\}$$

M =
3

$$
P=\{18,16,12,10,8,6,4,2\} $$

n(P)=
8

$$
B=\{Blue, Green, Red\}
$$

n(B)=
3

$$
C=\{Soccer, Football, Band, Band, Tennis\}
$$

C =
5

$$
E=\{\}
$$

E =
0


What is the null set?

The last example has a special name, it is known as the
empty
or
null
set. This set contains
no
elements.
Number Sets
Ther are several symbols that mathematicians use to reprsent commonte infinite sets.
Symbol 
Set 
Examples 
Notes 
$$ \mathbb{N} $$

Natural

$$ 1,2,3,4, $$

$$n_0 , N$$

$$ \mathbb{Z} $$

Integer

$$ 1, 0 , 1, 2 $$

$$Z^+ , Z^ $$

$$ \mathbb{Q} $$

Rational

$$ 1.75,\frac{1}{2} , \frac{3}{4} $$


$$ \mathbb{R} $$

Real

$$ \pi, \sqrt{3} $$


Practice with Sets of Number Types
Directions: Only click on the corresponding cells below that represent a the set each number is an element of. When you are done, check your work by hitting the "Check Answers" button.
Number 
$$ \mathbb{N} $$ 
$$ \mathbb{Z} $$

$$ \mathbb{Q} $$

$$ \mathbb{R} $$

2





1.75 




$$\frac{3}{4}$$ 




$$ 2\pi $$ 




$$\sqrt{5}$$ 




$$\frac{7}{1}$$ 




$$\sqrt{25}$$ 




2




