Inclusion-Exclusion via Multisets - Data Structures in Mathematics Math Foundations

Explore the theorem of Inclusion/Exclusion in Set Theory through an unorthodox lens focusing on multisets rather than traditional sets in this 48-minute video lecture. Delve into a unique approach that reduces the theorem to its arithmetic counterpart and apply it to the Euler phi function. Expand your understanding of multisets to include integral_msets, where element multiplicities can be any integer, not just natural numbers or zero. Discover how this broader perspective allows for differences between multisets, providing the flexibility needed for a conceptual and general statement of the Inclusion/Exclusion theorem. Learn about multiset operations such as sums, unions, intersections, and differences, and gain insights into the modern interpretation of negative numbers in counting exercises.

Introduction
Integral Msets
Subtraction
Proof for integers
Multiset sizes