Floor Function/Examples/Floor of -1.1

Theorem

 * $\left\lfloor{-1 \cdotp 1}\right\rfloor = -2$

where $\left\lfloor{x}\right\rfloor$ denotes the floor of $x$.

Proof
We have that:
 * $-2 \le -1 \cdotp 1 < -1$

Hence $-2$ is the floor of $-1 \cdotp 1$ by definition.

Also see

 * Floor of $1\cdotp 1$: $\left\lfloor{1 \cdotp 1}\right\rfloor = 1$
 * Ceiling of $-1\cdotp 1$: $\left\lceil{-1 \cdotp 1}\right\rceil = -1$