Floor Function/Examples/Floor of -1.1

Theorem

 * $\floor {-1 \cdotp 1} = -2$

where $\floor x$ 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 $1 \cdotp 1$: $\floor {1 \cdotp 1} = 1$
 * Ceiling of $-1 \cdotp 1$: $\ceiling {-1 \cdotp 1} = -1$