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Lecture 2022-02-08. 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…
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Injective, surjective, and bijective functions. Examples. Two methods to shuffle cards. Countably infinite sets.
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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…
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More about sets. Powerset of a set. Cross product of sets. The axiomatic approach to set theory. Languages (sets of strings).
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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,…
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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…
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