Definition:Quotient (Algebra)
From ProofWiki
Definition
Let $a, b \in \Z$.
From the Division Theorem, we have that:
- $\forall a, b \in \Z, b \ne 0: \exists! q, r \in \Z: a = q b + r, 0 \le r < \left|{b}\right|$
The value $q$ is defined as the quotient of $a$ on division by $b$, or the quotient of $\dfrac {a}{b}$.
something is wrong here
You can help ProofWiki by explaining it.
To discuss this point in more detail, feel free to use the talk page.
If you are able to explain it, then when you have done so you can remove this instance of {{Explain}} from the code.
If you would welcome a second opinion as to whether your explanation is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
When $x, y \in \R$ the remainder is still defined:
- $\forall x, y \in \Z, y \ne 0: \exists! q \in \Z, r \in \R: a = q b + r, 0 \le r < \left|{b}\right|$
See the definition of the Modulo Operation.
