Greatest Integer:

Greatest Integer: Any real number x may usually think of relaying between two consecutive integers can define P and P+1. i.e. P  ≤  x < (P + 1). That denotes, there forever exist an integer, say 'P' which is just less than or similar to x. That unique 'P' is known as the greatest integral value of x and is symbolically defined as [x] i.e. [x] stands for the greatest integer that is less than or similar to x.

e.g.  x = 3.54 => 3 < x < 4  => [x] = 3, x = -2.95 => -3 < x < -2 => [x] = - 3

It is clear that if x is integer, then [x] = x.

Important point

Fractional Part:

Fractional Part of any real number is described as the difference between the number 'x' and it's integral value '[x]' and is symbolically shown as {x}.

Therefore,  {x} = x - [x], e.g. if x = 5.68, then [x] = 5 and {x} = 0.68.

            If x is an integer => x = [x] => {x} = 0 => {[x]} = 0

If x∈[0,1) , then [x]=0 => {x}=x

            x∈[1,2) , then [x]=1=>{x}=x-1

Importasnt point

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