Explore advanced arithmetic concepts involving negative multisets (msets) in this 40-minute mathematics lecture. Delve into the world of box arithmetic using anti-msets to define negative numbers through explicit examples. Discover how integers are used not only as coefficients but also as exponents for polynumbers, introducing a crucial symmetry often overlooked in traditional algebra courses. Learn about Laurent polynomials as pure objects of analysis, and understand their significant impact on algebraic understanding. Follow along as the lecture covers topics such as anti-objects, negative msets, integer arithmetic, polynumber arithmetic, multiplicative operations with integer polynumbers, and arithmetic with integral (Laurent) polynumbers. Gain valuable insights into this fundamental mathematical concept that will enhance your understanding of algebra and its applications.