a conventional symbol denoting a number.
The earliest and most primitive way of writing numbers is the use of words. In a few cases this method was retained for a considerable time; for example, some mathematicians in Middle Asia and the Middle East made systematic use of a verbal notation in the tenth century and even later. As peoples developed socially and economically, the use of number words proved to be an inefficient form of notation. Better methods of symbolizing numbers were needed, and principles for representing numbers had to be developed (seeNUMERATION SYSTEM). As Figure 1 shows, different peoples developed different sets of numerals.
The oldest known numerals are those of the Babylonians and Egyptians. Babylonian numerals were used from the second millennium B.C. to the beginning of the Common Era. The numbers one, ten, and, sometimes, 100 were represented by particular cuneiform characters; other natural numbers were expressed by combinations of these basic symbols. The Egyptian hieroglyphic system of numerals developed between 3000 B.C. and 2500 B.C. It had a separate symbol for each power of ten from 100 to 107. Later, in addition to the hieroglyphic script, the Egyptians used the more cursive hieratic notation, which had more symbols—for example, symbols for multiples of 10 up to 100. In about the eighth century B.C the hieratic forms of the numerals were largely supplanted by demotic forms.
Similar to the Egyptian hieroglyphic system of numeration are the Phoenician, Syrian, Palmyrene, and Greek Attic (or Herodianic) systems. Attic numerals came into use in the sixth century B.C. In Attica they were used until the first century A.D., but in other Greek lands they gave way to the more convenient Ionian numerals, which are alphabetic. In the Ionian system a letter was assigned to each of the first nine integers, the first nine integral multiples of ten, and the first nine integral multiples of 100; the remaining numbers up to 999 were represented by combinations of these letters. Such numerals were first used in the fifth century B.C.
Other peoples employing alphabetic systems of numerals included the Arabs, Syrians, Hebrews, Georgians, and Armenians. The Old Russian system of numeration, which arose in about the tenth century and was still encountered in the 16th century, was also alphabetic; it used Cyrillic and, in rare instances, Glagolitic letters (seeSLAVIC NUMERALS).
Of the ancient numeral systems, the Roman lasted the longest. It originated circa 500 B.C. among the Etruscans and in some cases is still used today (seeROMAN NUMERALS).
The forerunners of the modern numerals, including a zero, appeared in India, probably not later than the fifth century A.D. Until then, Kharoshthi numerals had been used in India, along with a system of numerals similar to the letters of the Brahmi alphabet. Numeral forms from inscriptions found in the caves at Nasik are shown in Figure 1. Hindu numerals spread from India to other countries because of the convenience of representing numbers with such numerals in a decimal positional numeration system. Between the tenth and 13th centuries Hindu numerals were brought to Europe by the Arabs—hence the modern name “arabic numerals.” They came into general use in the second half of the 15th century. The appearance of Hindu-Arabic numerals has undergone substantial changes with the passage of time (see Figure 2). The early history of these numerals remains poorly investigated.
a nominal, the general lexical meaning of which is a quantity of persons or things. Grammatically, numerals are marked for the category of case (in languages with a developed morphology) and for gender (in languages with grammatical gender, some numerals possess marked forms; for example, Russian dva, “two” [masculine and neuter], and dve, “two” [feminine]) and are not marked for the category of number.
In Russian, numerals may be definite (dva, “two,” desiat’, “ten”) or indefinite (mnogo, “many,” malo, “few”), depending on the nature of the quantitative expression. Collective numerals designate quantity as a group (dvoe, “two,” troe, “three,” platero, “five,” oba, “both”); they constitute a special group. The structure of Russian numerals may be simple (dva, “two,” tri, “three,” odinnadtsat’, “eleven”), compound (piat’desiat, “fifty,” sem’desiat, “seventy”), or complex (tridtsat’ shest’, “thirty-six,” sto desiat’, “one hundred ten”). Many scholars consider ordinals and the word odin (“one”) as adjectives; such words have forms marked for both number and grammatical gender. The words desiatok (“a group of ten”), sotnia (“a group of one hundred”), and tysiacha (“[a group of] one thousand”) are nouns, inasmuch as they have all the formal characteristics of a noun. In the development of the Slavic languages, some numerals originated from other parts of speech; for example, Russian piat’ (“five”) was classified as a noun. Numerals should be distinguished from other words with quantitative meaning.
V. A. VINOGRADOV