We start this video by reviewing some standard uses of numbers: to allow us to determine sizes of sets/msets, to determine the position of an element in a list, and to scale an mset. This third usage of numbers is very important, and we want to think about how to extend this from natural numbers to integers.https://www.youtube.com/watch?v=DMJeJp3RoWI
To do this we need to have a formulation of how numbers multiply msets. Then we will move to thinking about how negative numbers might multiply msets too!
In this video we introduce the idea of the anti of a mathematical object. This is a crucial, but perhaps surprising, ingredient in a systematic development of multisets as a basis for modern algebra.https://www.youtube.com/watch?v=gqjiDfiZjps