The Assets-Claims on Assets Equivalence in the Axiomatic Method
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WSEAS Transactions on Mathematics
abstract
The purpose of the study is to analyze the assets-claims on assets equivalence based on the dualconcept of monetary units and the axiomatic method. The methodology is analytical, rationalistic anddeductive; it uses axiomatic theory with set theory and predicate logic to test set equivalence. The axiomatictheory 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.
