Are floor functions always discontinous?

Like for floor(x)are they removable discontinuities.Are the continuous from the left and right. Please help I don't understand.

Floor functions don't have removable discontinuities, they have jump discontinuities. If you're referring to the greatest integer function, ?x?, that would be a floor function, which is closed on the left, open on the right [a, a+1), { a | a ∈ ? }