Modulo Operation/Examples/-100 mod 0

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 $8$