Return to Discrete
Unit 2.1

SET
THEORY

A Set is a collection of distinct objects. It is the most fundamental concept in mathematics. Before we can count, measure, or compute, we must first learn to group.

THE CONTAINER
"A pack of wolves,
a bunch of grapes,
or a flock of pigeons."
- Georg Cantor
[Image of venn diagram set operations]

Venn Logic

We manipulate sets using Operations. Just as arithmetic adds numbers, set theory unions and intersects collections.

Set Builder

Union

A ∪ B

Everything in A OR B (or both). The "Marriage" of sets.

AB
Set A
Intersection
Set B

The Language

Set

{ ... }

A well-defined collection of distinct objects.

Element

x ∈ A

An object that belongs to a set.

Subset

A ⊆ B

Set A is a subset of B if every element of A is also in B.

Empty Set

∅ or { }

A set containing no elements. The "zero" of set theory.

Cardinality

|A|

The number of elements contained in a set.

Universal Set

U

The set containing all objects under consideration.

Why This Matters?

Set Theory is the foundation of Databases (SQL). When you query a database, you are essentially performing Unions, Intersections, and Differences on massive sets of data rows.