Numbers and numerals are closely connected, but distinct, concepts. Numerals represent and symbolize numbers. Numbers themselves are abstract concepts that may or may not correlate to phenomena in the physical world.

Numerals are any symbols used to denote a number. Ancient societies began the practice of keeping written records thousands of years ago. Records indicating the quantities of things stored or sold would obviously have been of great use to the merchant class. A convenient and standardized system of symbols was, therefore, needed to meet such a requirement. Such a system is called a "numeral system". A numeral system is defined as a particular set of symbols and associated rules used to represent numbers. In past ages a variety of numeral systems have been employed, including "simple grouping systems" (e.g., Roman numerals), "multiplicative grouping systems" (e.g., Chinese-Japanese), and "ciphered systems" (e.g...