Floor Function/Examples/Floor of 1.1

Theorem

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

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

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

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

Also see

 * Floor of $-1\cdotp 1$: $\left\lfloor{-1 \cdotp 1}\right\rfloor = -2$
 * Ceiling of $-1\cdotp 1$: $\left\lceil{-1 \cdotp 1}\right\rceil = -1$