COMS W3203 Lecture 6: Proof by Counterexample, and Collections
29 Sep 2016
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Announcements: midterm 1 is 10/19 in-class 70 min, *open note, on topics 1 and 2. Logic and proofs, collections: classes that will be moved to fridays, 10/3 -> 10/7, 10/12 -> 10/14, 10/17 -> 10/21. To prove equalities or inequality just use your algebra background: example: if > 2 then % > + 1, direct proof, > 2, 1 > 1, % 1 > + 1, % > + 1. 1 + 1 > ( + 1) since > 2: another way to direct proof, > 2, % > 2, % > + 1. Number of ways to fill a committee: e. g. Number of possibilities of two-letter initials: permutation vs combination, we will talk about, ordered sets (lists, definition: a list is an ordered sequence of objects/elements in form (element 1, element 2, , element n) Length is number of elements, n-element list is list of n elements.
