Inversooniks

Inversooniks is a fictional class of algebraic structures introduced in speculative mathematics and modern fiction to model inverse processes that operate across two dual operations. In the imagined framework, an inversoonik consists of a nonempty set equipped with two binary operations, called op and inv, together with an identity element e. Each element has a quasi-inverse under the two operations, and the operations satisfy a small set of coherence conditions intended to mimic the behavior of inverses in more familiar algebraic systems, while relaxing strict associativity and homomorphism requirements to allow duality.

Etymology: The term combines the word "inverse" with the suffix -oonik, intended to evoke a plural class. It was coined by a fictional mathematician in contemporary speculative fiction.

In practice, inversooniks are used as a narrative and theoretical device to explore questions about reversal, causality, and duality. They appear in thought experiments and world-building exercises where processes can be undone or inverted at a structural level, sometimes in imagined computation or physics settings.

Properties: A hypothetical inversoonik supports:

- Dual operations producing a unit-like element under a coherence rule.

- Existence of inverses with respect to each operation under a relaxed set of axioms.

- Compatibility conditions that encode a form of duality between the two operations.

Applications and reception: As a fictional construct, inversooniks are discussed in online essays and speculative fiction circles as a tool for illustrating duality and reversibility. They are not part of established mathematical theory and have no formal theorems outside their respective narratives.

See also: inverse, dual numbers, inverse semigroup, duality in category theory.