Abstract
Counting has always been one of the most important operations for human be-ings. Naturally, it is inherent in economics and business. We count with the unique arithmetic, which humans have used for millennia. However, over time, the most inquisitive thinkers have questioned the validity of standard arithmetic in certain settings. It started in ancient Greece with the famous philosopher Zeno of Elea, who elaborated a number of paradoxes questioning popular knowledge. Millennia later, the famous German researcher Herman Helmholtz (1821-1894) [1] expressed reservations about applicability of conventional arithmetic with respect to physical phenomena. In the 20th and 21st century, mathematicians such as Yesenin-Volpin (1960) [2], Van Bendegem (1994) [3], Rosinger (2008) [4] and others articulated similar concerns. In validation, in the 20th century expressions such as 1 + 1 = 3 or 1 + 1 = 1 occurred to reflect important characteristics of economic, business, and social processes. We call these expressions synergy arithmetic. It is common notion that synergy arithmetic has no meaning mathematically. However in this paper we mathematically ground and explicate synergy arithmetic.
Highlights
IntroductionIn the 21st century, expressions such as 1 + 1 = 3 occurred to reflect important characteristics of economic and business processes
We count with the unique arithmetic, which humans have used for millennia
Books exist which use these expressions as metaphors (Archibald, 2014 [29]; Trott, 2015 [30]; The Business Book, 2014 [31])
Summary
In the 21st century, expressions such as 1 + 1 = 3 occurred to reflect important characteristics of economic and business processes It seems that this contradicts core mathematical axioms and is incorrect from a mathematical point of view. Irrational numbers and later imaginary numbers were firstly rejected Today these concepts are accepted and applied in numerous scientific and practical fields, such as physics, chemistry, biology and finance. Mathematicians objected by saying that there are no such functions in mathematics (cf., for example, von Neumann, 1955 [8]) Later they grounded utilization of these functions developing the theory of distributions and finding numerous new applications for this theory (Schwartz, 1950/1951 [4])
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