Equinumerusilla

Equinumerusilla is a hypothetical concept used in mathematical philosophy and informal expositions to discuss counting and symmetry within a structured universe. It denotes a property of a given structure in which finite subsets that share the same cardinality are guaranteed to be related by a preferred, canonical bijection drawn from a specified family. The idea is intended as a tool for thought experiments and illustrative discussion rather than as a standard theorem.

The name blends equinumerous (equal in number) with the diminutive suffix -illa, signaling a specialized or restricted form of equinumerosity.

Formalization of equinumerusilla is deliberately nonstandard and context-dependent. In a chosen domain, the principle would hold that for any two finite nonempty subsets A and B of the domain with |A| = |B|, there exists exactly one bijection f: A → B that is minimal under a fixed well-ordering of the class of all such bijections and that respects a predetermined symmetry constraint. Under this reading, the focus is on canonicity and uniqueness of the pairing rather than merely on the existence of a bijection.

Interpretations and uses of equinumerusilla tend to be pedagogical or speculative. It can help clarify what is meant by a canonical pairing of equal-sized subsets and provoke reflections on how structure, symmetry, and counting interact. It is not a widely adopted axiom in mainstream mathematics and is commonly described as a conceptual or illustrative device rather than a formal, widely used principle.

See also: equinumerosity, bijection, isomorphism.