The big step from polynumbers to multinumbers!! | Math Foundations 228 | N J Wildberger

We continue to develop a new kind of arithmetic, based on the data structure called a multiset, or mset for short. After a quick review of the last lecture, we investigate how to move from polynumbers, which are the embodiment of polynomials in one variable in this context, to multinumbers. This turns out to be a convenient framework for algebra over many variables, with an accompanying more flexible attitude towards notation. Our reward is a large scale enlargement of what "arithmetic" actually means. Computer Science, here we come! A big thanks to all my Patreon supporters, and to Members of the Wild Egg mathematics courses channel. Video Contents: (thanks to phi Architect) 00:00 introduction 2:10 Pure msets are formed with only [ ] 3:50 Basic principle: pure msets can be described completely, unambiguously 7:00 Operations on pure msets 7:20 Addition: dump the contents of added msets into a new mset 7:50 Multiplication: add distributed combinations of the contents of msets 10:15 Modifying polynumber terminology / notation 13:00 α0 ≡ [ 1 ] 14:00 α1 ≡ [ α0 ] 14:40 α1 is the first multinumber that is not a polynumber 15:00 Basic arithmetic with polynumbers 20:00 But there are more multinumbers! 21:05 More arithmetic examples 30:00 Algebra in variables - α0, α1, α2, ... - extend Poly to Bi Poly 33:20 creating a tight framework for Algebra 34:18 Next: on a strange vessel on uncharted waters? Here are the Insights into Mathematics Playlists: https://www.youtube.com/playlist?list=PL55C7C83781CF4316 https://www.youtube.com/playlist?list=PL3C58498718451C47 https://www.youtube.com/playlist?list=PL5A714C94D40392AB https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf https://www.youtube.com/playlist?list=PLIljB45xT85D94vHAB8joyFTH4dmVJ_Fw https://www.youtube.com/playlist?list=PL8403C2F0C89B1333 https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua https://www.youtube.com/playlist?list=PLIljB45xT85DH__ZzGQWQrVRxlbKh-Nsa https://www.youtube.com/playlist?list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8 https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF https://www.youtube.com/playlist?list=PLIljB45xT85DSrlV6NX8RMBksZhdTHtwW https://www.youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7 Here are the Wild Egg Maths Playlists (some available only to Members!) https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB https://www.youtube.com/playlist?list=PLzdiPTrEWyz4VlOppC5CN0D0GjrjvBGKy https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG- https://www.youtube.com/playlist?list=PLzdiPTrEWyz6zpIZ4Y_RK9zyJ9OufqNJv https://www.youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6 https://www.youtube.com/playlist?list=PLzdiPTrEWyz5j1BJdXBw1MFst_nQAqzZ_ https://www.youtube.com/playlist?list=PLzdiPTrEWyz5HWgaVkhIwpGVKi6fciRxW https://www.youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM https://www.youtube.com/playlist?list=PLzdiPTrEWyz7LKbuJAHaXAhRj2ylD0OoX https://www.youtube.com/playlist?list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM https://www.youtube.com/playlist?list=PLzdiPTrEWyz6MwUTOHRgC0oIxVtaHGQBd https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS https://www.youtube.com/playlist?list=PLzdiPTrEWyz4IknbwXMEVwxOWS3z1Ch3C ************************