5. The ceiling of a real number x, denoted by [x], is the unique integer that...

 

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5. The ceiling of a real number x, denoted by [x], is the unique integer that satisfies the inequality [x] – 1<x< [x]. In words, [x] is the smallest integer that is greater than or equal to x. Answer the next two questions about the ceiling of a number. a) Compute [0.1], [-1.7] and [ (6.3 - [5.7 + [-4.8]]) 1 (1 mark) b) Prove or disprove the following. Show all your work if this is true. Show a counter example if it is not true. For any real number x, if [x]- x > 1/2 then [2x] = 2[x] - 1 (3 marks) 5. The ceiling of a real number x, denoted by [x], is the unique integer that satisfies the inequality [x] – 1<x< [x]. In words, [x] is the smallest integer that is greater than or equal to x. Answer the next two questions about the ceiling of a number. a) Compute [0.1], [-1.7] and [ (6.3 - [5.7 + [-4.8]]) 1 (1 mark) b) Prove or disprove the following. Show all your work if this is true. Show a counter example if it is not true. For any real number x, if [x]- x > 1/2 then [2x] = 2[x] - 1 (3 marks)

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