A multiset approach to arithmetic | Math Foundations 227 | N J Wildberger

We introduce a new framework for basic arithmetic and algebra, using the data structure of a multiset, or mset. This is an unordered collection of mathematical objects in which repetition is allowed. But what constitutes a "mathematical object"? One way of proceeding is to begin with the simplest possible mset, which is the empty mset, and build up from there. This is analogous to well -known treatments from set theory, but the consequences when we use msets instead are profound. We are able to give simple and natural inductive definitions of natural numbers, polynumbers, and higher extensions which we call multinumbers. Crucially the operations are also defined in a very general fashion. I'd like to thank my Patreon supporters for encouragement and helpful comments. Video Content: (Thanks to phi Architect) 00:00 Introduction and history of multiset development 4:20 A multiset (mset) is an unordered collection allowing repetitions 7:20 A natural number (NAT) is an mset of zeroes 9:40 A polynumber is an mset of natural numbers 11:55 A multinumber is an mset of polynumbers 14:40 Addition of msets 19:15 NAT is closed under addition and commutative, associative 21:40 Multinumbers are also closed under addition 22:20 Multiplication of msets of msets 31:00 Each "type domain" is closed under addition and multiplication 32:30 The meaning of "poly" 36:15 Distinction of mset and list 38:30 Mathematics as a topic in computer science 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 ************************