225_03_induction_lists

225_03_induction_lists - 1 Put your name if you want your...

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Unformatted text preview: 1 Put your name if you want your attendance credit. Please put your e-mail as well. CSC 225 is done at 11:30 so I did NOT fill in the box for 11:30 for our class. 2 Some students claimed to prove that 2k = 2 k+1 1. Try to prove by induction that: 2k = 2 k+1 1. Where does the proof go off-track? 3 If you are on my connex roster, you should have received an e-mail I sent out Monday reminding you to bring your schedule to class today. Please make sure you can access connex. Start work now on assignment #1. Please ask me questions if any of the instructions are not clear to you. Next tutorial: the lab instructor can answer any questions you have about induction, linked lists, class material or the assignment. Students who are slow in starting the assignment may benefit from hearing questions other students have. Note: you dont have to wait until the tutorial if you have questions. Ask me or send me e-mail. 4 n f(i) i=c Meaning of notation (translation to code): sum= 0; for (i=c; i n; i++) sum= sum + f(i); The value of the expression is sum at the termination of this loop. 5 = { 0, 1, 2, 3, 4, } Natural Numbers Inductive Definition: [Basis] 0 is in the set [Inductive step]: If k is in then k+1 is in 6 The idea behind the simplest form of an induction proof: Suppose we are given a statement S(n) and we want to show that S(n) is true for all integers n 0. If we prove: 1. that S(0) is a true statement, and 2. if S(n) is a true statement then so is S(n+1) then this is sufficient to prove that S(n) is true for all integers n 0. 7 k Theorem S(k): 2i = 2 k+1 - 1 i=0 Proof: [Basis] When k=0,...
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225_03_induction_lists - 1 Put your name if you want your...

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