What is least integer function Difference between greatest integer function and least integer function

Greatest integer function also called as the floor function is one of the generally used function in mathematics. The greatest integer function of a real number x is represented by [ x ] or | x |. This function is also known by the names of step or floor function. It returns the greatest integer less than or equal to x. Another way to understand it that the greatest integer function rounds down the values into the nearest integer possible. This function is piece wise defined. This function basically gives us the nearest integer value of the input as an output.It is represented by the square bracket ( [X] ). Definition of function is given below, f(x) = [X] = greatest integer <= Domain of function: {R}, set of real number Range: { I }, Set of integer value. Examples: [2.8] = 2 (greatest integer less than and equal to 2.8 ) [3.999] = 3 (greatest integer less than and equal to 3.999) [4] = 4 (as 4 is itself an integer, remember the equal to sign) [-5.99] = -6 (the greatest integer less than -5.99 is -6, remember the sign less than or equal to). Smallest integer function also called as Ceil function is one of the generally used function in mathematics. This function basically, gives us the nearest integer value of the input as an output. It is represented by the square bracket ( [X] ). Definition of function is given below, f(x) = [X] = smallest integer Domain of function: {R}, set of real number Range: { I },Set of integer value. Examples: [2.8] = 3 (smallest integer greater than and equal to 2.8 ) [3.999] = 4 (smallest integer greater than and equal to 3.999) [4] = 4 (as 4 is itself an integer, remember the equal to sign) [-5.99] = -5(smallest integer greater than and equal to -5.99 is -5) For any real number x, this step function is defined by, f(x) = |x| where, the smallest integer is greater than or equal to x. For example, [4.75] = 5, [-7.2] = -7, [4] = 4. read less