Original sentence: For any two elements a and b in M:.In mathematics, monus, also written as a minus sign with a dot above, is an operation defined on the elements of an ordered commutative monoid (M, 0, +, <) as follows:.a monus b = 0 if a < b, and.a monus b = a − b if a ≥ b
Edited sentence: 0 otherwise.If for any a ≤ b there exists a (unique) smallest element c such that a + b =c, then M is called a commutative monoid with monus.In a commutative monoid with monus, the monus a −b of any two elements a and b is defined as follows:.In mathematics, monus is a variant of subtraction that can be defined for certain commutative monoids that are not groups.Since this relation is a preorder in every monoid, the condition amounts to saying that the relation is antisymmetric, i.The monus a − b of two elements a and b (also written with a dot above the minus sign) is defined in certain commutative monoids M such that the relation defined by a ≤ b if and only if there is another element c such that a + b =c is a partial order.a − b = the smallest c such that a + b =c if a ≤ b, or.if a ≤ b and b ≤ a then a = b