Class 10: In(tro)duction

cs2102: Discrete Mathematics
University of Virginia, Fall 2016

See course site for notes:
https://uvacs2102.github.io

Transcript

1. Class 10: In(tro)duction cs2102: Discrete Mathematics | F16 uvacs2102.github.io David Evans | University of Virginia
2. Plan Finish Power Sets Proof by Well-Ordering Principle Induction Principle Induction Examples
3. My Grading Scale «Gold Star – Excellent Work – got everything I wanted out of this «Green Star – Got most things I wanted, but some answers could be better «Silver Star – Some serious problems
4. Unbounded Expectations! «« - exceptional work «««- better than I thought possible ««««- breakthrough! «««««- deserve a Turing Award!
6. Grades do not have denominators! Scores are not “out of” anything. Point of the assignments is for learning, not for taking of points.
7. Well-Ordering Proofs What can we conclude at the end of a well-ordering principle proof?
8. Power Set Size To use well-ordering (or induction!) need a proposition like: ∀ ∈ ℕ. Goal: ∀ ∈ . = 2|3|
9. Power Set Size Prove ∀ ∈ ℕ. pow ℕ7 = 27
13. Induction Principle
15. Induction Principle To prove ∀ ∈ ℕ. : 1. Prove (0). 2. Prove ∀ ∈ ℕ. ⟹ ( + 1). Prove ∀ ∈ ℕ. pow ℕ7 = 27
16. Slack poll: Induction vs. Well-Ordering Principle Also: any questions about content on PS4
18. Why prefer one proof technique?
19. Prove by Induction: ℕ is well-ordered.
20. Charge • PS4 Due Friday (6:29pm) • Next week: – “Strong” Induction (MCS 5) – Induction Practice