Show that if x is a real number, then

Chapter 1, Problem 49E

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QUESTION:

Show that if \(x\) is a real number, then \(x-1<\lfloor x\rfloor \leq x \leq\) \(\lceil x\rceil<x+1\).

Equation Transcription:

 

 

Text Transcription:

x  

x−1<⌊x⌋ < or =x  < or = ⌈x⌉<x+1

Questions & Answers

QUESTION:

Show that if \(x\) is a real number, then \(x-1<\lfloor x\rfloor \leq x \leq\) \(\lceil x\rceil<x+1\).

Equation Transcription:

 

 

Text Transcription:

x  

x−1<⌊x⌋ < or =x  < or = ⌈x⌉<x+1

ANSWER:

Solution:

Step 1:

           In this problem we need to show that

                                           , where x is a real number.

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

                     

                       

                     

                       

         Example :  

                 

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