Greatest Integer Function

In the previous post we have discussed about Define Sector of a Circle and In today's session we are going to discuss about Greatest Integer Function.Function are widely used in mathematics. Greatest integer function is one of them, it is also known as the names of floor function or step functions. Here in this blog we are going to discuss the greatest integer function. The greatest integer function for a real number x can be denoted as [x] or [_x_]. This function returns the greatest integer that is less than or equal to x. To be more precise, it rounds downward the rates into closest integer.
[4.9] = 4 (greatest integer less than and equal to 4.9)
[2.99] = 2 (greatest integer less than and equal to 2.99)
[6] = 6 (6 itself as an integer)
[-4.87] = -5 (greatest integer less than -4.87 is -5)
You should remember that all of the above examples are based on a rule that is a greatest integer will be less than or equal to x.
To understand greatest integer function we can plot function on the graph paper.
Example 1: - Determine the greatest integer function for the given numbers.
1.1, 7, -4.8, 2 and -3.6
Solution: -
We have 1.1, 7, -4.8, 2 and -3.6 real numbers.
[1.1] = closest greatest integer value is less than 1.1 is 1.
[1.1] = 1
[7] = 7 is itself an integer that is equal to x so
[7] = 7
[-4.8] = in this closest greatest integer is -5 which is less than -4.8
[-4.8] = -5
[2] = 2 is itself an integer that is equal to x so
[2] = 2
[-3.6] = in this closest greatest integer is -4 which is less than -3.6
[-3.6] = -4

The greatest integer function is defined piecewise.

The area of a circle formula is ∏r ². It helps us to find the area of circle. ICSE class 10 books covers  all the  syllabus in a very  organized and  effective  manner