Definition:Modulo Operation/Modulo Zero

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Definition

Let $x, y \in \R$ be real numbers.

Let the modulo operation $\bmod$ be defined as:

$x \bmod y := \begin{cases} x - y \left \lfloor {\dfrac x y}\right \rfloor & : y \ne 0 \\ x & : y = 0 \end{cases}$


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