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.

A = {x, y, z}
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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