Least Integer Function, Ceiling function, graph, limit, continuity

In this video the topic of least integer function is completely covered. Least integer function is a very important topic for examination. In this lecture Qais Ali Khan explains the topic of least integer function completely. Moreover, Qais Ali Khan explains the definition of least integer function and he solves some examples of least integer function. Then he explains why is the least integer function called the ceiling function and why is the greatest integer function called the floor function. He solves examples for integers and non integer inputs of least integer function. Then he shows that the answer of least integer function and greatest integer function is the integer itself if that integer is the input of the function. After this, Qais Ali Khan explains the graph of least integer function. After the graph of least integer function Qais Ali Khan explains the limit of least integer function and explains that why limit does not exist at the integer points in the least integer function. After limit Qais Ali Khan explains the continuity of the least integer function from the graph and he explains the continuity of least integer function at integer and non integer points. Moreover, Qais Ali Khan show that on integer points the limit of least integer function does not exist and the function is also discontinuous at these integer points.