Empty, Finite, and Infinite Sets
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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