The Assets-Claims on Assets Equivalence in the Axiomatic Method

The purpose of the study is to analyze the assets-claims on assets equivalence based on the dual
concept of monetary units and the axiomatic method. The methodology is analytical, rationalistic and
deductive; it uses axiomatic theory with set theory and predicate logic to test set equivalence. The axiomatic
theory involves a set of axioms, which are used in combination with accounting axioms to develop a proof of the assets-claims on the assets considered as finite sets. The analysis uses a bijective function based on the dual concept of monetary units, and proof by contraposition to test the fulfillment of the requirement of a bijective mfunction. Results show that assets cardinality is not equal to claims on assets cardinality when taking into account the dual concept of monetary units, and as a consequence assets and claims on assets are not equivalent.