Humans have always needed to measure and desired to measure phenomenon in order to understand it better, seemingly have some control over it. Even cavemen must have understood the basic concept of measuring and counting, for man is not an island, sharing and rewarding requires an understanding of the need to measure and count. Obviously the mathematics of today is far more sophisticated than the cavemen’s concept.
This paper seeks to look into the mathematical concept of infinity and does it have a role in economics. Any science, including economics, must adapt tools to its own needs. This paper seeks to show why the mathematical concept of infinity at times needs to be adapted when dealing with economics in particular and many other sub disciplines of other sciences in general. This paper will illustrate that often, continuous functions, can not be interpreted the same, each function does not adhere in the same manner to the concept of infinity. The purely mathematical abstract of infinity (being abstract, like an abstract painting, it should have limitations placed on it or removed), can not always suite the needs of non abstract concepts. Cantorian theory when applied in particular to economics can often lead to misleading models. This paper will show that the philosophy behind Cantor’s set theory of numbers can not be universally applied, because many times it does not make logical sense.
The paper concludes by showing that understanding the mathematical concept of infinity will itself lead to a different understanding of the mathematical derivative and a must needed revision of the mathematical derivative when dealing with units that can not be split into infinitely many parts.
This paper aims to show that if economists are to be scientists rather than merely mimicking science, they must challenge accepted concepts for their own needs, adapt the concepts in a scientifically accepted manner for their ends, thus contributing to the main body of science.