for a challenge involving the mathematical operator of division or integer division
Division is the inverse of multiplication on a skew field.
In a skew field division is a binary operator applied to two non-zero elements to produce a single element of the field.
For example in the modular arithmetic Z5
3 / 2 = 4
where / is the division operation.
This is because in Z5
4 * 2 = 3
Most often challenges tagged division will operate on the field Q (the rational numbers) or some subset of R (the real numbers).
Integer Division is a generalization of Division onto all rings. Given an element a such that
a = (p * q) + r, r < q
Integer division is the binary operation between a and q that yields p.
a // q = p
where // is the integer division symbol.
On a skew field r will always be the additive identity and thus the result of Integer division and division will always be the same.
Integer division is most common on the ring I (the integers), being the reason it is named Integer division. On I Integer division can be thought of as the floor of the corresponding division on Q.
