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Show that if x is a real number, then if x is not an

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 48E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 48E

Show that if x is a real number, then   if x is not an integer and if x is an integer.

Step-by-Step Solution:
Step 1 of 3

Step-1:

     In this problem we need to show that

                                                   , if x is not an integer

  And

            , if x is an integer.

NOTE: The symbols for floor and ceiling are like the square brackets [ ] with the top or bottom part missing.

                     

                       

                       

                       

Example :  

                 

Step-2:

Case(1): If x is not an integer.

Let us consider , , where a is an integer and .

Then ,

   

 ...

Step 2 of 3

Chapter 2.3, Problem 48E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Show that if x is a real number, then if x is not an

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