Floor Function/Examples/Floor of 1.1

Theorem

$\floor {1 \cdotp 1} = 1$

where $\floor x$ 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.

$\blacksquare$

Also see

• Floor of $-1\cdotp 1$: $\floor {-1 \cdotp 1} = -2$
• Ceiling of $-1\cdotp 1$: $\ceiling {-1 \cdotp 1} = -1$

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory: Exercise $1$