Definition:Quotient (Algebra)

Definition
Let $a, b \in \Z$ be integers such that $b \ne 0$.

From the Division Theorem:


 * $\forall a, b \in \Z, b \ne 0: \exists_1 q, r \in \Z: a = q b + r, 0 \le r < \left|{b}\right|$

The value $q$ is defined as the quotient of $a$ on division by $b$, or the quotient of $\dfrac a b$.

Real Arguments
When $x, y \in \R$ the quotient is still defined:

Also see

 * Definition:Integer Division
 * Definition:Remainder