Definition:Modulo Operation/Modulo Zero
Jump to navigation
Jump to search
Definition
Let $x, y \in \R$ be real numbers.
Let the modulo operation $\bmod$ be defined as:
- $x \bmod y := \begin {cases} x - y \floor {\dfrac x y} & : y \ne 0 \\ x & : y = 0 \end {cases}$
Then:
- $\forall x \in \R: x \bmod 0 = x$
This can be considered as a special case of the modulo operation, but it is interesting to note that most of the results concerning the modulo operation still hold.
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: $(1)$