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
/ is the division operation.
This is because in Z5
4 * 2 = 3
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
q that yields
a // q = p
// 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.