The Accounting Equation Inequality: A Set Theory Approach

The basics of financial accounting in the balance sheet and the accounting equation are revisited from the viewpoint of axiomatic set theory and predicate logic. The conceptual distinction between assets and claims on the assets are pointed out; next, it follows an application of the axioms of the theory. By a combination of axioms, this application leads to obtain two sets of capital units, which contains assets and claims (Liabilities plus Owners’ Equity) on the assets, respectively. These sets are properly built, according to the use of the axioms; they contain all the lowest level items of the financial statements that still have financial meaning in the balance sheet. An analysis of the equality between these sets was applied to test the equality of the assets to the union of liabilities and equity. The analysis determined that these sets were not equal and as a conclusion assets are not equal to liabilities plus equity. This inequality is interpreted within the restrictions of the application of the set theory to financial data and algebraic sum. Nevertheless, the particular case where the accounting equation holds is described; however, this case has no financial meaning.