Floor Function/Examples/Floor of 0.99999

Theorem

$\floor {0 \cdotp 99999} = 0$

where $\floor x$ denotes the floor of $x$.


Proof

We have that:

$0 \le 0 \cdotp 99999 < 1$

Hence $0$ is the floor of $0 \cdotp 99999$ by definition.

$\blacksquare$


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 $1$
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