What are the axioms of Combinatorics? Does it have a set of well-defined axioms? Because most Combinatorial solutions are not formulated in a mathematical manner (at least those I have seen) and contain a considerable portion of natural language and mostly refer to "obvious" things. Is Combinatorics axiom-less or every Combinatorial solution is a logical conclusion of axioms?
2026-04-04 07:00:22.1775286022
Axioms of Combinatorics
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There are some principles in combinatorics, like
equality principle (sets for which there is a bijection between them have the same cardinality).
addition principle: $|\bigcup_i A_i| = \sum_i |A_i|$ for sets which are pairwise disjoint.
multiplication principle: $|\prod_i A_i| = \prod_i |A_i|$.