


Lecture 20220208. Equinumerous sets. Another proof that the rationals are countable. Uncountability of the set of all languages over {0,1}. When do things become impractical? Concrete dividing…


Injective, surjective, and bijective functions. Examples. Two methods to shuffle cards. Countably infinite sets.


Review of strings and languages. Closing a set of languages using some operators. Regular languages. Examples. BYTE, WORD32, and WORD64 as languages computers "like", and how we…


More about sets. Powerset of a set. Cross product of sets. The axiomatic approach to set theory. Languages (sets of strings).


NOTE: "Typo" in what I wrote on one slide: R={x: x \not\in x}. Basics of sets. The only basic vocabulary is \in and \emptyset. Defining other relations: union, intersection complement,…


Basics of sets. The only basic vocabulary is \in and \emptyset. Defining other relations: union, intersection complement, set difference, symmetric difference. Identities and their proofs, including…


















