Definition:Modulo Operation

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

Then the modulo operation is defined and denoted as:
 * $x \bmod y := \begin{cases}

x - y \floor {\dfrac x y} & : y \ne 0 \\ x & : y = 0 \end{cases}$

where $\floor {\, \cdot \,}$ denotes the floor function.

Modulo 0
We see that, from the definition:

Modulo 1
Note also that from the definition:

Also see

 * Definition:Floor Function
 * Definition:Fractional Part
 * Definition:Quotient (Algebra)
 * Definition:Remainder


 * Definition:Congruence (Number Theory) which approaches the subject from a slightly different direction.