Category:Definitions/Dipper Operations

This category contains definitions related to Dipper Operations.
Related results can be found in Category:Dipper Operations.

The dipper operation $+_{m, n}$ is the binary operation on $\N_{< \paren {m \mathop + n} }$ defined as:

$\forall a, b \in \N_{< \paren {m \mathop + n} }: a +_{m, n} b = \begin{cases}

a + b & : a + b < m \\ a + b - k n & : a + b \ge m \end{cases}$ where $k$ is the largest integer satisfying:

$m + k n \le a + b$