1. “Step functions” are sometimes used to describe real-life situations.
Our book refers to one such function:
This is the Greatest Integer Function.

2. Greatest Integer Function:

3. Greatest Integer Function:

4. Greatest Integer Function:

5. Greatest Integer Function:

6. Greatest Integer Function:
The greatest integer function is also called the floor function.
The notation for the floor function is:
This notation was introduced in 1962 by Kenneth E. Iverson. .
Recent by math standards!

7. Least Integer Function:

8. Least Integer Function:

9. Least Integer Function:

10. Least Integer Function:

11. Least Integer Function:
Don’t worry, there are not wall functions, front door functions, fireplace functions!
The least integer function is also called the ceiling function.
The notation for the ceiling function is: