Numeraalide

Numeraalide, or numerals, are symbols used to express numbers within a numeral system. They function as written representations of quantities; the same numeral can denote different values in different systems, and a single abstract number may be written with many different numeral forms.

The most widely used system today is the Hindu-Arabic decimal system, which is base-10 and uses digits 0 through 9 plus a zero placeholder and place value. This system underpins daily arithmetic, science, and commerce, and it allows compact representation of very large or very small numbers through positional notation and decimal fractions.

Historically, numeral ideas have appeared independently in several cultures. Tally marks and counting boards served as early gauges of quantity, while more formal numeral systems evolved in places such as Mesopotamia, Egypt, and India. Hindu-Arabic numerals, including the concept of zero, were developed in India and spread through the Islamic world to Europe, where they gradually supplanted earlier methods by the end of the medieval period.

Numerals are used for cardinal numbers (one, two, three) and ordinals (first, second, third), dates, measurements, and calculations. In writing, numerals can be decimal digits or other symbols, and many languages share the same digits while employing different conventions for grouping and punctuation. Non-positional and base systems, such as Roman numerals, illustrate alternative ways of encoding numbers without place value, while modern computing frequently relies on binary and other bases. The distinction between numerals (symbols) and numbers (abstract quantities) remains fundamental in mathematics.