EXPLAIN ABOUT GREATEST INTEGER FUNCTION.IN DETAIL

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

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Regards,

Askiitians Experts

Mohit Singla