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Functions

☼ Integer Part Function [ x ] OR Floor Function ⌊x⌋ :–

f : R → Z, f (x) = ‘ the greatest integer not greater than x ’ is called an Integer Part Function and it is denoted by [ x ] .

It is also called a Floor Function. And it is denoted by . i.e. f (x) = [ x ] = ⌊x⌋

☼ Ceiling Function ⌈x⌉ :–

f : R → Z, f (x) = ‘ the smallest integer not smaller than x ’ is called a Ceiling Function and it is denoted by ⌈x⌉ . i.e. f (x) = ⌈x⌉

☼ Identity Function :–

I_A : A → A, I_A (x) = x is called an Identity Function.

☼ Signum Function :–

f : R → { –1, 0, 1 }, f (x) = $\left\{\begin{matrix}1:x>0\\0\ :x=0\\-1\ :x<0\\\end{matrix}\right.$ is called a Signum Function.