,
lim
( )
lim [ ]
[ ]
x
c
x
c
f x
x
c
→
=→
= Also f(c) = [c] and hence the function is continuous at all real
numbers not equal to integers Case 2 Let c be an integer Then we can find a sufficiently small real number
r > 0 such that [c – r] = c – 1 whereas [c + r] = c