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01:25:00 ECS20 - W22 - Lecture 12 (6R): Induction and… ECS20 - W22 - Lecture 12 (6R): Induction and Recursion 1	ECS20 - W22 - Lecture 12 (6R): Induction and Recursion 1 Lecture 2022-02-10. The language of number theory, and the Peano axioms for it. The last axiom: the principle of mathematical induction. Different forms of it. Using induction for establishing… induction mathematical induction peano axioms basis inductive step inductive assumption triominoes envelopes times packs thing numbers n. sum hand proof side assumption step trauma grid packets successor cubed symbol From Phil Rogaway 0 likes 118 plays 0
01:21:17 ECS20 - W22 - Lecture 7 (4T): Sets 2 ECS20 - W22 - Lecture 7 (4T): Sets 2	ECS20 - W22 - Lecture 7 (4T): Sets 2 More about sets. Powerset of a set. Cross product of sets. The axiomatic approach to set theory. Languages (sets of strings). sets langauges powerset cross product kleene closure regular language string strings language cross alphabet languages power characters elements length element things comma operator thing b. axioms theory numbers From Phil Rogaway 0 likes 106 plays 0
01:22:02 ECS20 - W22 - Lecture 4 (2R): Logic 3 ECS20 - W22 - Lecture 4 (2R): Logic 3	ECS20 - W22 - Lecture 4 (2R): Logic 3 Building a circuit for adding two 64-bit values. Tautologies. A formal system for proving theorem. The completeness and soundness theorems for sentential logic. Adding quantifier: first-order… circuit adder tautology formal proofs completeness soundness first-order logic formula truth logic table bit proof kind universe phi assumptions statement variables carry statements axioms function english symbol From Phil Rogaway 0 likes 149 plays 0
05:55 ECS 220 6c:7.2-2 From undecidable problems to… ECS 220 6c:7.2-2 From undecidable problems to unprovable truths	ECS 220 6c:7.2-2 From undecidable problems to unprovable truths statement rules proof axioms inference statements proofs contradiction reasoning thing systems hilbert 30s bit answer algorithm string kind negation properties From David Doty 0 likes 16 plays 0