IST4_lec9

IST4_lec9 - IST 4 Information and Logic 1 M1 31 6 2 6 5 26...

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Unformatted text preview: IST 4 Information and Logic 1 M1 31 6 2 6 5 26 19 M2 5 4 12 4 5 3 M2 28 3 2 21 2 1 14 M1 7 fri thr wed tue mon IST 4: Planned Schedule – Spring 2008 x= hw#x out x= hw#x due = today T Mx= MQx out Mx= MQx due midterms midterms T Factoradic to Permutation: see animation on the class web site HW#3: I hope you Started ??????? Done ??????? Factoradic and Permutations 1 2 3 4 5 0,1,2 0,2,1 1,0,2 1,2,0 2,0,1 2,1,0 decimal permutation Lexicographic order? The range is 0- 5 In general the range is 0-(n! -1) 1 2 3 4 5 0,1,2 0,2,1 1,0,2 1,2,0 2,0,1 2,1,0 decimal permutation factoradic 000 010 100 110 200 210 2 0 1 1 1 1 0 0 2 copy if smaller increase by 1 if bigger or equal decimal to factoradic to permutations? decimal to permutations? Factoradic and Permutations The last digit in the factoradic representation is always 0 and is omitted 0x0! We introduce it for the sake of the transformation (so we have n digits) 2 4 3 2 2 1 1 3 1 2 4 1 3 5 1 2 5 4 3 6 1 copy if smaller increase by 1 if bigger or equal Factoradic and Permutations We augment a 0 Which number is encoded with the following permutation? 1 4 2 5 6 3 copy if smaller decrease by 1 if bigger 3 1 4 5 2 1 3 4 2 1 3 2 1 2 1 Factoradic and Permutations 1 4 2 5 6 3 3 1 4 5 2 1 3 4 2 1 3 2 1 2 1 Factoradic description: Factoradic and Permutations What is the 5039 permutation on 7 elements? 7! – 1 = 5039 6543210 So Far The logical sense = number sense = 3 number system = syntax to extend our number sense Boolean algebra = syntax to extend our logical sense Proofs are FUN… especially when they are short … and correct ... Boole was never a student at a university… only a professor… Leibniz never held an academic position… The Babylonian never did homework sets... Current state Proof Flow Proof Flow Proof Flow Proof Flow Proof Flow A1-A4 L1 T1 T2 T3 L2 T4 T0 Proof Dependency A1-A4 L1 T1 T2 T3 L2 T4 T0 Proofs are Syntax manipulation A1-A4 L1 T1 T2 T3 L2 T4 T0 Does not work: not allowed to use the ‘future’ in the ‘present’......
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This note was uploaded on 12/12/2009 for the course IST 4 taught by Professor Shuki during the Spring '09 term at Caltech.

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IST4_lec9 - IST 4 Information and Logic 1 M1 31 6 2 6 5 26...

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