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

## Problem 48E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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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

Step 3 of 3

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