# 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| = $$S=\{20,13,0,-5\}$$ |S| = $$M=\{15,15,15\}$$ |M| = $$P=\{18,16,12,10,8,6,4,2\}$$ n(P)= $$B=\{Blue, Green, Red\}$$ n(B)= $$C=\{Soccer, Football, Band, Band, Tennis\}$$ |C| = $$E=\{\}$$ |E| =

# 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 $$\mathbb{N}$$ $$\mathbb{Z}$$ $$\mathbb{Q}$$ $$\mathbb{R}$$

## 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