MIT6_042JS10_lec03

MIT6_042JS10_lec03 - 1/30/10 Mathematics for Computer...

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1/30/10 1 Lec 2M.1 Albert R Meyer February. 8, 2010 This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License . Mathematics for Computer Science MIT 6.042J/18.062J The Well Ordering Principle Lec 2M.2 Albert R Meyer February. 8, 2010 Well Ordering principle Every nonempty set of nonnegative integers has a least element. Familiar? Now you mention it, Yes. Obvious? Yes. Trivial? Yes. But watch out: Lec 2M.3 Albert R Meyer February. 8, 2010 Every nonempty set of has a Well Ordering principle rationals NO! Lec 2M.4 Albert R Meyer February. 8, 2010 Well Ordering principle Every nonempty set of has a NO! Lec 2M.11 Albert R Meyer February. 8, 2010 Well Ordering Principle Proofs To prove using WOP: define set of counterexamples assume C is not empty. By WOP, have minimum element Reach a contradiction somehow usually by finding with c < m n N . P(n) C :: = n N | NOT P(n) { } m C c C Lec 2M.12 Albert R Meyer February. 8, 2010 available stamps: Thm: Get any amount n Prove by WOP.
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MIT6_042JS10_lec03 - 1/30/10 Mathematics for Computer...

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