The document explains the greatest integer function, denoted as f(x) = [x], which represents the largest integer less than or equal to x. It provides examples of how the function operates with various inputs and discusses properties such as graph, domain, range, and differentiability. The function is noted to be non-differentiable across the real numbers but differentiable between integers.

1. GREATEST INTEGER FUNCTION

2. Greatest Integer
Function
The greatest integer value of point ‘a’ is a smallest integer from a
but greater than all value.
It is denoted by f(x) = [x]. [x] = the greatest integer less than or
equal to x
Examples: [3.7] = 3 [9.9] = 9 [0.5] = 0
[-3.7] = -4 [-9.9] = -10 [-0.5] = -1
f(x) = [x] =

3. Graph of Greatest Integer Function

4. Domain and Range

5. Monotonicity

6. Periodicity

7. Boundedness

8. Graph of Greatest Integer Function

9. Continuity

10. Uniformly Continuity

11. Differentiability
• The function is not differentiable in R.
• This function is differentiable in (a,b) if a & b are integers.

12. Riemann Integral