# The Accounting Equation Inequality: A Set Theory Approach

## Article excerpt

ABSTRACT

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.

JEL: G3, M2, M4

KEYWORDS: Corporate Finances, Financial Accounting, Balance Sheet, Accounting Equation, Set Theory

(ProQuest: ... denotes formulae omitted.)

INTRODUCTION

The balance sheet is based on the equality of assets to liabilities plus owners' equity. This equation is the fundamentals of the financial statements and analysts make significant efforts to classify items and fit the equation. However, it is well-known that different views in financial accounting analysis lead to different financial decision-making as it happens regarding conservatism accounting (Wang, 2013). According to Wang, conservatism involves the prudence principle and its application results in asymmetric different timeliness for recognizing earnings and losses. Therefore, it shows the influence of the figures significance; subjectivity is associated with numbers and changes the financial operations.

Accounting report analysis also contains different approaches. The semiotic linguistic theory analyzes the accounting reports as texts rather than from an economic viewpoint (Macintosh and Baker, 2002). Macintosh and Baker use an approach based on the notion of heteroglossic novel, where accounting has a representational nature; this approach uses the perspective of the literary theory in the analysis of accounting data. Accordingly, it calls for a conversational rather than a monologic process of accounting and, again, the diverse interpretations of accounting information are significant.

Chaos and complexity theories provide a different approach to financial statements and financial accounting. Lewin (1999) explored the implications of complexity in management studies, and Richardson (2008) pointed out that the metaphorical language is a characteristic of the sciences of complexity in management. According to the use of complexity theory in management and corporate finances, financial statements are not a fixed structure but a complex dynamic system. This system comprises many processes and various subsystems located at different levels, interacting with each other and resulting in a proper fit (Juárez, 2013). Juárez (2013) described how the use of belief logic (see belief logic in Smullyan, 1986) is implicit in the management discussion & analysis section and notes of the financial statements. The manner that the analyst communicates the findings in these sections is relevant; it is a communicative act where results depend on the type of reasoning used. In this line, belief and paraconsistent logics are tools that help in the analysis and conclusion of these sections (see Juárez, 2012, 2013, 2014).

Historically, it has been an interest in reviewing the foundations of financial accounting; in 1967, Sterling discussed the theoretical basis of accounting. …

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