Cartesian product
Date: 2025-12-13
The Cartesian product is a function that takes an ordered pair of sets and maps it to a set of ordered pairs of their elements.
It is a set construction operation that combines elements from two sets into ordered pairs.
For any two sets A and B, the Cartesian product A × B is the set of all possible ordered pairs where the first element belongs to A and the second element belongs to B.
Let A and B be sets
The Cartesian product is denoted by ×
×:(A,B)→C, where C is the set of all pairs and each pair contains the first element from A and the second from B
Given functions that take a set and return some of its elements. We will not name them, but will create a functional diagram
As we defined pair already we have
A ← (A,B) → B
so
A ← (A,B) → B
↓ ↓ ↓
a ← (a,b) → b
where a belongs to A and b belongs to B
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