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.

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!

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Screenshot PDFs for my videos are available at the website [ Ссылка ]. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at [ Ссылка ]

My blog is at [ Ссылка ], where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at [ Ссылка ] Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at [ Ссылка ] Your support would be much appreciated.

Here are the Insights into Mathematics Playlists:

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