Modulo Operation/Examples/-100 mod 0
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Theorem
- $-100 \bmod 0 = -100$
where $\bmod$ denotes the modulo operation.
Proof
By definition of modulo $0$:
- $\forall x \in \R: x \bmod 0 = x$
Hence:
- $-100 \bmod 0 = -100$
$\blacksquare$
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 $8$