### Abstract

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.

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.

Original language | English (US) |
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Pages (from-to) | 431 - 440 |

Number of pages | 10 |

Journal | WSEAS Transactions on Mathematics |

Volume | 15 |

State | Published - 2016 |

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### Cite this

Juarez Acosta, F. (2016). The Assets-Claims on Assets Equivalence in the Axiomatic Method.

*WSEAS Transactions on Mathematics*,*15*, 431 - 440 .