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by: Nick Rowe

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Foundations Of Computer Science CS 18200

Marketplace > Purdue University > ComputerScienence > CS 18200 > Foundations Of Computer Science
Nick Rowe
Purdue
GPA 3.68

Wojciech Szpankowski

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COURSE
PROF.
Wojciech Szpankowski
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

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This 2 page Class Notes was uploaded by Nick Rowe on Saturday September 19, 2015. The Class Notes belongs to CS 18200 at Purdue University taught by Wojciech Szpankowski in Fall. Since its upload, it has received 90 views. For similar materials see /class/208061/cs-18200-purdue-university in ComputerScienence at Purdue University.

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Date Created: 09/19/15
Existential Quanti er Universal Quanti er Binomial Coe icient Product Logarithm De nition Properties Things to Know77 There exists an x such that Pm is true 3P For all m Pm is true WWW The number of m combinations of a set of n distinct objects n 71 m mln7ml H fjfifi1 fk iSiSk Z f0fifi1fk iSiSk Formgt07 log xyltgt 2ym L1 Log is a strictly increasing function Vz7 gt y a log z gt log y L2 Log is a oneto one function L3 log 1 0 L4 L5 L6 L7 L8 Summation Properties Vz7 ylog z log y a m y Va logz 2 a Vzhy logm y log z log y Vz7a log z a log z Vm7ymlog y ylog 1 logo N logo I 10gb N L1 Let f be any function7 then L2 L3 L4 L5 L6 17 2 111 17 17 1 91 2110 291 17 b Zf1fab1 altb 1 n M 2 Proof by induction Base Step for 11 17 1 2i 11 1 1 11 2 Induction Hypothesis Assume that for some 1 gt 07 TL 11 1 lt 7 7 V11 7 k 21 2 11 Inductive Step 1 4 11 1 11 1n2 21ltZ1gt111 2 111 2 11 11 TL 21 2711 1 10 11 Ziz 11111621117 n 1 11 Proof by Induction Base Step for 11 17 1 11121 1 6 12 11 Inductive Step Assume for some 1 gt 0 that n 11 11 1 n 2 V11 g k W then 111112111 n1n22n11 lggn 1SlIZSTLzZHnH f n f f

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