It helps me to compare sign relations with my other favorite class of triadic relations, namely, groups. Applications of mathematical groups came up just recently in the Laws of Form discussion group, so it will save a little formatting time to adapt the definition used there.
Definition 1. A group is a set together with a binary operation satisfying the following three conditions.
- Associativity. For any
- Identity. There is an identity element such that
- Inverses. Each element has an inverse, that is, for each
there is some such that