The Finite Capacity-Based System is a mathematical framework built on axioms of strict finiteness: it assumes a universal limit (capacity) on set sizes and numeric precision, and even treats probability as a fundamental principle, rather than ever postulating actual infinities. Unlike traditional infinite-set mathematics (which relies on unbounded sets and the axiom of infinity), this system never steps beyond the finite realm – it can reproduce classical results (e.g. calculus limits or large combinatorial outcomes) through finite approximations, yet always remains within fixed finite bounds. By confining all structures to discrete, finite entities, it ensures every operation is rigorously computable and will terminate, so each computation stays exact and fully verifiable within bounded resources. Practically, aligning math with real hardware limits in this way avoids issues like rounding errors, overflows, or infinite loops, making programs based on these principles more robust, efficient, and easier to debug and verify.
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