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This course examines natural numbers together with 0 under addition, union, and intersection, using multisets as motivation. It proves identity, order, subtraction, and distributive laws, including a variant connected to tropical calculus.
Syllabus
Multisets and natural number arithmetic
Properties of natural numbers
Identity Laws
Proofs of the various properties
Order Laws
Are the various laws independent?
Subtraction
A variant of a distributive law
Proof of the theorem
Taught by
Insights into Mathematics