# Types of Sets — Set Theory

*This is a continuation of my previous post about Set Theory. If you have not read it yet, start **there**.*

### Empty Sets

One of the most obvious type of sets is an empty set — `∅`

. Empty set is considered to be a subset of all other sets.

`$10_bills_in_my_wallet = ∅`

### Singleton Sets

A set with one element is considered to be a singleton set. Remember, a singleton set may have one subset with many elements in it.

`{{a, b, c}}`

is a singleton set

### Unordered Pair

A set with exactly two elements with no significance in their order is an unordered pair.

`{left, right} = {right, left}`

### Ordered Pair

A set with exactly two elements in order is an ordered pair.

`(1, 2) ≠ (2 ,1)`

### Power Set

A power set is a special set that returns all subsets that can be formed from a given set.

When

A = {x, y, z}

then

𝒫(x) = {∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}

As it can be seen from the above example, the power set of a set with `n`

elements would yield 2ⁿ subsets.

*Originally published at **medium.com** on September 14, 2017.*