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Set Cardinatlity

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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
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What is the null set?

The last example has a special name, it is known as the or set. This set contains elements.

Number Sets

Ther are several symbols that mathematicians use to reprsent commonte infinite sets.
Symbol Set Examples Notes
$$ \mathbb{N} $$
$$ \mathbb{Z} $$ $$Z^+ , Z^- $$
$$ \mathbb{Q} $$
$$ \mathbb{R} $$
set  of common number types

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.
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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
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