1. What is Cartesian Product?

The Cartesian product (also called set multiplication) of two sets A and B is the set of all ordered pairs (a, b) where a is in A and b is in B. It's fundamental in mathematics, particularly in set theory, relations, and database theory.

2. How Does the Calculator Work?

The calculator computes the Cartesian product using:

Process:

1. Input is split into elements by commas
2. Empty elements are removed
3. Each element from set A is paired with each element from set B
4. Results are displayed as ordered pairs

3. Importance of Cartesian Product

Applications: Used in database joins (SQL), coordinate systems, relations in discrete mathematics, and as the basis for constructing more complex mathematical structures.

4. Using the Calculator

Tips: Enter elements separated by commas. Spaces around commas are allowed and will be trimmed. Example: "1, 2, 3" or "red,green,blue".

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Cartesian product and regular multiplication?
A: While both combine elements, Cartesian product creates ordered pairs rather than numerical products.

Q2: Does order matter in Cartesian product?
A: Yes, A × B is different from B × A unless A = B. The ordered pairs (a,b) and (b,a) are different when a ≠ b.

Q3: What if a set has duplicate elements?
A: The calculator treats duplicates as distinct elements, so they will appear in the result.

Q4: How many elements are in A × B?
A: If A has m elements and B has n elements, then A × B has m × n elements.

Q5: Can I compute Cartesian product of more than two sets?
A: This calculator handles two sets, but mathematically you can extend to n sets (A × B × C × ...).