Number: The Language of Science

Abstract

AbstractAlthough every schoolchild today learns number representation and the basic arithmetic operations on decimals at an early age, the concept of a fully-symbolized number itself is far from elementary. This is the topic of the present chapter. It begins with a discussion of symbolization in human language and then proceeds to the symbolization of number. Mathematicians have developed a proper understanding of the latter and of resulting number systems only quite recently during the past four centuries. Some of these number systems are discussed, namely, cardinal integers, signed integers, rational numbers, and reals, along with their symbolic representation using different bases. Historical background is presented, and a contrast drawn between symbol-based and magnitude-based representation of numbers. The structure underlying the foregoing basic number systems was subsequently extended, generalized, or relaxed by mathematicians, leading to other systems of numbers, for example, complex, algebraic, and hyperreal, and to other key mathematical concepts, thereby evolving over time into the highly elaborated mathematics of today. The metaphorical phrase, “under the rubric of number,” refers to this overarching umbrella of mathematics.