# Are ceiling and floor elementary functions?

According to the Wikipedia entry on elementary functions, the trigonometric functions and their inverses are elementary functions.

It doesn't seem to me that the floor and ceiling functions should be elementary, since they don't seem too natural. However, here is an expression of the floor function using only elementary functions

$$\text{floor}(x) = (x - 0.5)-\frac{\arctan(\tan(\pi(x-0.5)))}{\pi}$$

As pointed out below, this function is undefined for the integers.

Here is a plot of this function using Desmos. I am aware that this is not proof of this identity, and that this identity depends on the choice of range for $\arctan$. However, given that $\arctan$ was listed as an elementary function on the Wikipedia entry, I assumed that this was independent of the choice of range.

Is there anything I am missing here? Or is floor, and therefore ceiling and modulo all elementary functions?