## Semiotics, Semiosis, Sign Relations • Comment 3

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 $(G, *)$ is a set $G$ together with a binary operation $* : G \times G \to G$ satisfying the following three conditions.

1. Associativity.  For any $x, y, z \in G,$
we have $(x * y) * z = x * (y * z).$
2. Identity.  There is an identity element $1 \in G$ such that $\forall g \in G,$
we have $1 * g = g * 1 = g.$
3. Inverses.  Each element has an inverse, that is, for each $g \in G,$
there is some $h \in G$ such that $g * h = h * g = 1.$

cc: Category Theory • Cybernetics (1) (2)
cc: Ontolog ForumStructural ModelingSystems Science
cc: FB | SemeioticsLaws of Form • Peirce List (1) (2) (3) (4) (5) (6)

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