What is a numeral system?

A numeral system is a mathematical notation and writing system used to express numbers without words using digits or symbols. Different systems use positional notation or sign-value notation, meaning the same sequence of symbols can represent entirely different values depending on the system used. Over human history, notations have evolved from simple fingers and tally marks to sophisticated positional systems like the globally prevalent decimal system.

What we know

• A numeral system is a writing system for expressing numbers without words through mathematical notation. [3]
• The same sequence of symbols can represent different values in different numeral systems, such as the string "11" representing eleven in decimal, three in binary, and two in unary. [3]
• Ancient numeral systems such as Roman, Greek, and Egyptian numerals lack an official representation for zero. [3]
• Numeral systems progressed from fingers and tally marks dating back more than 40,000 years to early notations in Mesopotamia around 5,000 to 6,000 years ago. [4]

Where to go next

• whenHow did ancient numeral systems develop?
• a case in pointHow does the Hindu-Arabic numeral system work?
• compared withWhat distinguishes number systems from numeral systems?
• how it workedHow do computers use the binary numeral system?
• the bigger pictureWhat are writing systems used for across human history?
• an unexpected connectionHow did a 13th-century Italian book help spread decimal numbers in Europe?Fibonacci's Liber Abaci played a major role in bringing the Hindu-Arabic numeral system from Arabic mathematics into medieval Europe.

Sources

• [1]list of numeral systems (Wikidata Q3634986) · CC0 1.0
• [2]List of numeral systems · CC BY-SA 4.0
• [3]Numeral system · CC BY-SA 4.0
• [4]History of ancient numeral systems · CC BY-SA 4.0
• [5]Hindu–Arabic numeral system · CC BY-SA 4.0