Recognizing Set Types — Select which sets are finite and which are infinite!

{1,2,3,4,5} and the empty set are finite, the set of natural numbers and even numbers are infinite.

Empty, Finite, and Infinite Sets

Subsets and Proper Subsets Set Operations

Sets can also be grouped according to how many elements they contain. The most important types: empty set, finite set, and infinite set.

Empty Set

The empty set contains no elements at all. Notation: ∅ or {}.

Example: The set of natural numbers that are both less than 5 and greater than 5 is an empty set.

Finite Set

A finite set is one whose elements are countable, and their number is finite.

Example: The set of the first ten natural numbers is finite.

Infinite Set

An infinite set contains infinitely many elements, meaning it is impossible to count all its elements.

Example: The set of natural numbers is infinite because there is no largest natural number.

Everyday Examples

Empty set: the set of books that are both 1000 pages and 200 pages long.
Finite set: the colors of the rainbow {red, orange, yellow, green, blue, indigo, violet}.
Infinite set: the set of all even numbers {2,4,6,8,...}.

Practice Exercise

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