hw1 - b x c is de²ned as the largest integer that is less...

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CprE 310 Theoretical Foundations of Computer Engg, Spring 08 Homework 1 Due: 31 Jan 2008, In class Problem 1.1 Prove the following statement. For any natural number k 1, if 3 k + 7 is odd, then k must be even. Problem 1.2 We know (from class) that 2 is irrational. Using this fact, prove that 25 37 2 is irrational. Problem 1.3 Construct a set S such that Each element of S is a real number between 0 and 1 S has no minimum element and S has no maximum element Problem 1.4 For any real number x , the “±oor of x ”, denoted by the symbol
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Unformatted text preview: b x c is de²ned as the largest integer that is less than or equal to x . For example, b 3 . 5 c = 3, b-2 . 5 c =-3 and b 1 c = 1. This function is commonly used in computer algorithms, and there is also a “C” function called floor which implements the above de²nition. Prove or disprove the following statement. For every real number x , b 3 x c = 3 b x c . Problem 1.5 Prove the following statement. For any natural number x ≥ 1, x 2-1 can never be a perfect square....
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This note was uploaded on 03/26/2008 for the course CPR E 310 taught by Professor Srikanta during the Spring '08 term at Iowa State.

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