Equal is strict identity: the condition that two expressions denote exactly the same thing, with no room for structural variation or contextual relativity. It is the strongest notion of sameness in the relational framework.
Equal operates across all five movements as a utility condition. It provides the strict identity used throughout the derivation whenever two expressions must be the same thing — as in the idempotence of Close (closing what is already closed changes nothing), the cubic return of Iterate (three self-applications restore the original), and the KZ-Lax inequalities governing Flow.
Equal is reflexive (a thing is always equal to itself), symmetric (if a equals b then b equals a), and transitive (if a equals b and b equals c then a equals c). In a relational framework where things are constituted through their relations, strict extensional equality is a strong condition. The weaker notion Equivalent is often more natural, since it respects structural sameness — two things can play the same role without being literally the same object.
Related
- Equivalent — the weaker, context-sensitive notion of sameness