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EXPLAIN ABOUT GREATEST INTEGER FUNCTION.IN DETAIL

EXPLAIN ABOUT GREATEST INTEGER FUNCTION.IN DETAIL

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1 Answers

Askiitians Expert Mohit Singla
19 Points
10 years ago

Dear Love,

Greatest integer function returns the greatest integer less than or equal to a real number.
The greatest integer function(GIF) is denoted by the symbol “[x]”.
In terms of integral and fraction parts, we write a real number "x" as :

x=[x]+{x}.

Here  [x]=integral part

  and {x}=fractional part.


     The fractional part is defined as  0≤{x}<1

Considering different cases:

Case 1: x>0

Say x=2.5

Here x= 2 + 0.5

i.e. integral part = 2 = GIF

and  fractional part=0.5

Case 2:x<0

Say x=-2.5

Here We break x= -3 + 0.5

Because  0≤{x}<1

Therefore (GIF)=-3=integral part.

and  fractional part=0.5


The value of "[x]" is an integer (n) such that :

f(x)=[x]=n;ifn≤x<n+1  ,n belongs to Integer

Thus a  two step process :

If “x” is an integer, then [x] = x.
If “x” is not an integer, then [x] evaluates to greatest integer less than “x”.

For graph and examples on Greatest Integer Function Please refer to the link

http://www.askiitians.com/iit-jee-algebra/set-relations-functions/greatest-integer-function.aspx


Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.


All the best Love !!!

 
Regards,

Askiitians Experts

Mohit Singla

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