Fulminantset

Fulminantset is a term used in speculative mathematics and science fiction to denote a class of sets that exhibit explosive growth under a defined enlargement operation. The term is not part of the established mathematical canon, and its precise meaning varies by author or context. The name derives from the adjective fulminant, meaning sudden and severe, to convey the notion of rapid expansion.

In a hypothetical formal framework, a fulminantset S within a given universe U is equipped with an enlargement operator F. Starting with S0 = S and iterating Sn+1 = F(Sn), the sequence of sets grows in a way that is not bounded by any fixed polynomial in n. Equivalently, there exists a superpolynomial growth function g(n) such that the size of Sn exceeds g(n) for infinitely many n. A common fictional construction defines F so that F(S) equals the power set of S, giving |F(S)| = 2^{|S|}, with subsequent iterations producing hyper-exponential growth under standard interpretations of power-set enlargement.

In practice, fulminantset is often employed as a device to illustrate ideas about rapid combinatorial expansion, emergent complexity, or limits of computation within constrained systems. Variants of the concept appear in discussions of growth rates, explosive growth in combinatorics, and hierarchies built from repeated applications of a growth operator.

Because fulminantset is a hypothetical construct rather than a rigorously standardized notion, there are no universal axioms or theorems associated with it. As a result, definitions, examples, and properties are context-dependent and can differ across sources. Related ideas include exponential growth, hyperoperation sequences, and the study of growth rates in formal systems.