Universal #1292

Legacy number: 1292

 Number  1288
 Original  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.
 Formula  subtraction &/v division ⇒ addition & multiplication
 Keywords  numeral
 Domain  word formation
 Type  implication
 Status  achronic
 Quality  absolute
 Basis  56 languages mentioned in Greenberg 1978a
 Source  Greenberg 1978a: 257 (#9)

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Discussion
Notes
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.
Comment
Frans Plank · 3 Aug 2006
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. <a class="innerLink" href="browse.php?entry_id=1252"><img src="../img/entry.gif" border="0">