# 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.

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