Of the four fundamental arithmetical operations –addition and its inverse, subtraction, and multiplication and its inverse, division –the existence of either inverse operation implies the existence of both direct operations.
Standardized
IF a numeral system has subtraction and/or division, THEN it has addition and multiplication.
1. As the only known alternative arithmetical operation beyond these fundamental ones, Greenberg refers to the so-called “going-on” operation, which is found in some Mayan and Finno-Ugric languages. Ostyak (Ugric, Uralic) expresses 18 as 8, 20, that is ‘8 going-on 20’. (Hurford 1975: 235 called this operation “over-counting”, which seems to be the more common expression; cf. Comrie 1997: 53).2. Cf. #1252.
1. As the only known alternative arithmetical operation beyond these fundamental ones, Greenberg refers to the so-called “going-on” operation, which is found in some Mayan and Finno-Ugric languages. Ostyak (Ugric, Uralic) expresses 18 as 8, 20, that is ‘8 going-on 20’. (Hurford 1975: 235 called this operation “over-counting”, which seems to be the more common expression; cf. Comrie 1997: 53).2. Cf. #1252.