Clearly this
function is defined for every real number For a fixed real number c, we have
lim
( )
( )
x
c p x
p c
→
=
By definition, p is continuous at c Since c is any real number, p is continuous at
every real number and hence p is a continuous function Example 15  Find all the points of discontinuity of the greatest integer function defined
by f (x) = [x], where [x] denotes the greatest integer less than or equal to x