Let n be any integer

[x] = Greatest integer less than or equal to x.

Some values of [x] for specific values of x

[3] = 3

[4.4] = 4

[-1.6] = -2

Therefore,

Left hand limit at x = n

= = n – 1

Right hand limit at x = n

= = n

Also, f(n) = [n] = n

As

Therefore, f(x) = [x] is discontinuous at x = n.