884:; a clay envelope shaped like a hollow ball into which the tokens on a string were placed and then baked. If anybody contested the number, they could break open the clay envelope and do a recount. To avoid unnecessary damage to the record, they pressed archaic number signs on the outside of the envelope before it was baked, each sign similar in shape to the tokens they represented. Since there was seldom any need to break open the envelope, the signs on the outside became the first written language for writing numbers in clay, using sign-value notation.
803:
Although signs may be written in a conventional order the value of each sign does not depend on its place in the sequence, and changing the order does not affect the total value of the sequence in an additive system. Frequently used large numbers are often expressed using unique symbols to avoid
739:
using a sequence of numerals which each represent a distinct quantity, regardless of their position in the sequence. Sign-value notations are typically additive, subtractive, or multiplicative depending on their conventions for grouping signs together to collectively represent numbers.
825:
represents numbers by a series of numerals in which signs representing smaller values are typically subtracted from those representing larger values to equal the value of the number represented. In Roman numerals, for example,
876:
to represent a number of a specific commodity, and strung the tokens like beads on a string, which were used for accounting. There was a token for one sheep and a token for ten sheep, and a different token for ten goats, etc.
771:
891:
often utilised different signs to count or measure different things, and identical signs could be used to represent different quantities depending on what was being counted or measured. Eventually, the
868:
When ancient people wanted to write "two sheep" in clay, they could inscribe in clay a picture of two sheep; however, this would be impractical when they wanted to write "twenty sheep". In
1011:(2017). "Evolutionary Complexity of Social Cognition, Semasiographic Systems, and Language". In Mufwene, Salikoko S.; CoupƩ, Christophe; Pellegrino, FranƧois (eds.).
838:
means nine (10 ā 1). The consistent use of the subtractive system with Roman numerals was not standardised until after the widespread adoption of the
788:
are added together to represent a larger number. To represent multiples of the sign value, the same sign is simply repeated. In Roman numerals, for example,
718:
1095:
438:
887:
Initially, different systems of counting were used in relation to specific kinds of measurement. Much like counting tokens, early
Mesopotamian
1048:
1020:
808:, for example, use a tally of dots for numbers less than twenty alongside unique symbols for powers of twenty, including 400 and 8,000.
851:
271:
1078:
747:
of each sign is independent of its position, the value of the sequence as a whole may depend on the order of the signs, as with
62:
856:
Sign-value notation was the ancient way of writing numbers and only gradually evolved into place-value notation, also known as
505:
1038:
909:
711:
286:
631:
641:
458:
518:
784:
represents numbers by a series of numerals that added together equal the value of the number represented, much as
614:
383:
1119:
1066:
1008:
888:
704:
31:
694:
478:
75:
378:
294:
16:
This article is about a class of numeral signs. For the sociological/economic concept of sign value, see
496:
921:
591:
452:
445:
326:
860:. Sign-value notations have been used across the world by a variety of cultures throughout history.
926:
857:
673:
489:
301:
233:
88:
49:
586:
339:
176:
171:
118:
1074:
1044:
1034:
1016:
775:
668:
658:
646:
626:
581:
576:
512:
344:
316:
223:
156:
146:
133:
98:
93:
1030:
873:
571:
465:
218:
206:
151:
141:
108:
83:
683:
653:
596:
566:
551:
311:
279:
251:
228:
211:
70:
1015:. Cambridge approaches to language contact. Cambridge, U.K.: Cambridge University Press.
663:
839:
817:
805:
752:
748:
744:
678:
621:
601:
556:
429:
161:
128:
113:
39:
21:
1113:
764:
484:
373:
306:
246:
181:
123:
103:
881:
880:
To ensure that nobody could alter the number and type of tokens, they invented the
636:
561:
893:
869:
785:
606:
471:
423:
413:
763:"Additive notation" redirects here. For the convention for abelian groups, see
1099:
408:
166:
17:
905:
901:
897:
418:
403:
388:
736:
393:
1013:
Complexity in
Language: developmental and evolutionary perspectives
770:
769:
398:
360:
321:
800:
means eighty (50 + 10 + 10 + 10).
900:-using cultures. The sexagesimal sign-value system used by the
1103:
974:
972:
947:
945:
943:
929:, a base 2 sign-value notation invented by J. Napier in 1617
20:. For a representation of signed numbers in computers, see
751:
which combine additive and subtractive notation, such as
755:. There is no need for zero in sign-value notation.
908:would later evolve into the place-value system of
978:
963:
951:
712:
8:
1043:. New York, U.S.: Oxford University Press.
818:Roman numerals Ā§ Subtractive notation
719:
705:
55:
26:
939:
38:
990:
835:
831:
827:
797:
793:
789:
7:
852:History of ancient numeral systems
14:
1:
1073:. University of Texas Press.
910:Babylonian cuneiform numerals
896:system was widely adopted by
765:Abelian group Ā§ Notation
1098:for Decimal/Roman Numerals (
1040:The World's Writing Systems
979:Daniels & Bright (1996)
964:Daniels & Bright (1996)
952:Daniels & Bright (1996)
1136:
849:
815:
762:
439:Non-standard radices/bases
15:
1067:Schmandt-Besserat, Denise
889:proto-cuneiform numerals
695:List of numeral systems
1071:How Writing Came About
804:excessive repetition.
778:
850:Further information:
774:Additive notation in
773:
63:HinduāArabic numerals
922:Place-value notation
823:Subtractive notation
812:Subtractive notation
592:Prehistoric counting
368:Common radices/bases
50:Place-value notation
927:Location arithmetic
858:positional notation
733:sign-value notation
539:Sign-value notation
966:, p. 796ā797.
779:
195:East Asian systems
1050:978-0-19-507993-7
1031:Daniels, Peter T.
1022:978-1-107-05437-0
782:Additive notation
776:Egyptian numerals
759:Additive notation
729:
728:
528:
527:
1127:
1096:Online Converter
1084:
1054:
1026:
994:
988:
982:
976:
967:
961:
955:
949:
872:they used small
837:
833:
829:
799:
796:means fifty, so
795:
791:
721:
714:
707:
510:
494:
476:
466:balanced ternary
463:
450:
56:
27:
1135:
1134:
1130:
1129:
1128:
1126:
1125:
1124:
1120:Numeral systems
1110:
1109:
1092:
1081:
1065:
1062:
1060:Further reading
1057:
1051:
1035:Bright, William
1029:
1023:
1007:
1003:
998:
997:
989:
985:
977:
970:
962:
958:
950:
941:
936:
918:
866:
854:
848:
820:
814:
768:
761:
749:numeral systems
725:
689:
688:
611:
597:Proto-cuneiform
542:
541:
530:
529:
524:
523:
508:
492:
474:
461:
448:
435:
364:
363:
351:
350:
331:
291:
276:
267:
266:
257:
256:
238:
197:
196:
187:
186:
138:
80:
66:
65:
53:
52:
40:Numeral systems
25:
12:
11:
5:
1133:
1131:
1123:
1122:
1112:
1111:
1108:
1107:
1091:
1090:External links
1088:
1087:
1086:
1079:
1061:
1058:
1056:
1055:
1049:
1027:
1021:
1009:Croft, William
1004:
1002:
999:
996:
995:
993:, p. 111.
983:
981:, p. 798.
968:
956:
954:, p. 796.
938:
937:
935:
932:
931:
930:
924:
917:
914:
865:
862:
847:
844:
840:printing press
834:means ten, so
830:means one and
813:
810:
806:Aztec numerals
792:means ten and
760:
757:
753:Roman numerals
745:absolute value
727:
726:
724:
723:
716:
709:
701:
698:
697:
691:
690:
687:
686:
681:
676:
671:
666:
661:
656:
651:
650:
649:
644:
639:
629:
624:
618:
617:
610:
609:
604:
599:
594:
589:
584:
579:
574:
569:
564:
559:
554:
548:
547:
546:Non-alphabetic
543:
537:
536:
535:
532:
531:
526:
525:
522:
521:
516:
503:
487:
482:
469:
456:
442:
441:
434:
433:
426:
421:
416:
411:
406:
401:
396:
391:
386:
381:
376:
370:
369:
365:
358:
357:
356:
353:
352:
349:
348:
342:
336:
335:
330:
329:
324:
319:
314:
309:
304:
298:
297:
295:Post-classical
290:
289:
283:
282:
275:
274:
268:
264:
263:
262:
259:
258:
255:
254:
249:
243:
242:
237:
236:
231:
226:
221:
216:
215:
214:
203:
202:
198:
194:
193:
192:
189:
188:
185:
184:
179:
174:
169:
164:
159:
154:
149:
144:
137:
136:
131:
126:
121:
116:
111:
106:
101:
96:
91:
86:
79:
78:
76:Eastern Arabic
73:
71:Western Arabic
67:
61:
60:
59:
54:
48:
47:
46:
43:
42:
36:
35:
22:Sign-magnitude
13:
10:
9:
6:
4:
3:
2:
1132:
1121:
1118:
1117:
1115:
1105:
1101:
1097:
1094:
1093:
1089:
1082:
1080:0-292-77704-3
1076:
1072:
1068:
1064:
1063:
1059:
1052:
1046:
1042:
1041:
1036:
1032:
1028:
1024:
1018:
1014:
1010:
1006:
1005:
1000:
992:
987:
984:
980:
975:
973:
969:
965:
960:
957:
953:
948:
946:
944:
940:
933:
928:
925:
923:
920:
919:
915:
913:
911:
907:
903:
899:
895:
890:
885:
883:
878:
875:
871:
863:
861:
859:
853:
845:
843:
841:
824:
819:
811:
809:
807:
801:
787:
783:
777:
772:
766:
758:
756:
754:
750:
746:
743:Although the
741:
738:
734:
722:
717:
715:
710:
708:
703:
702:
700:
699:
696:
693:
692:
685:
682:
680:
677:
675:
672:
670:
667:
665:
662:
660:
657:
655:
652:
648:
645:
643:
640:
638:
635:
634:
633:
632:Alphasyllabic
630:
628:
625:
623:
620:
619:
616:
613:
612:
608:
605:
603:
600:
598:
595:
593:
590:
588:
585:
583:
580:
578:
575:
573:
570:
568:
565:
563:
560:
558:
555:
553:
550:
549:
545:
544:
540:
534:
533:
520:
517:
514:
507:
504:
501:
500:
491:
488:
486:
483:
480:
473:
470:
467:
460:
457:
454:
447:
444:
443:
440:
437:
436:
431:
427:
425:
422:
420:
417:
415:
412:
410:
407:
405:
402:
400:
397:
395:
392:
390:
387:
385:
382:
380:
377:
375:
372:
371:
367:
366:
362:
355:
354:
346:
343:
341:
338:
337:
333:
332:
328:
325:
323:
320:
318:
315:
313:
310:
308:
305:
303:
300:
299:
296:
293:
292:
288:
285:
284:
281:
278:
277:
273:
270:
269:
265:Other systems
261:
260:
253:
250:
248:
247:Counting rods
245:
244:
240:
239:
235:
232:
230:
227:
225:
222:
220:
217:
213:
210:
209:
208:
205:
204:
200:
199:
191:
190:
183:
180:
178:
175:
173:
170:
168:
165:
163:
160:
158:
155:
153:
150:
148:
145:
143:
140:
139:
135:
132:
130:
127:
125:
122:
120:
117:
115:
112:
110:
107:
105:
102:
100:
97:
95:
92:
90:
87:
85:
82:
81:
77:
74:
72:
69:
68:
64:
58:
57:
51:
45:
44:
41:
37:
33:
29:
28:
23:
19:
1085:(Paperback).
1070:
1039:
1012:
991:Croft (2017)
986:
959:
886:
879:
867:
855:
822:
821:
802:
781:
780:
742:
732:
730:
538:
498:
459:Signed-digit
334:Contemporary
201:Contemporary
1001:Works cited
894:sexagesimal
874:clay tokens
870:Mesopotamia
864:Mesopotamia
842:in Europe.
786:tally marks
735:represents
637:Akį¹£arapallÄ«
607:Tally marks
506:Non-integer
1100:JavaScript
934:References
816:See also:
674:Glagolitic
647:Kaį¹apayÄdi
615:Alphabetic
519:Asymmetric
361:radix/base
302:Cistercian
287:Babylonian
234:Vietnamese
89:Devanagari
18:Sign value
906:Akkadians
902:Sumerians
898:cuneiform
642:Äryabhaį¹a
587:Kharosthi
479:factorial
446:Bijective
347:(IƱupiaq)
177:Sundanese
172:Mongolian
119:Malayalam
1114:Category
1069:(1992).
1037:(1996).
916:See also
904:and the
669:Georgian
659:Cyrillic
627:Armenian
582:Etruscan
577:Egyptian
485:Negative
345:Kaktovik
340:Cherokee
317:Pentadic
241:Historic
224:Japanese
157:Javanese
147:Balinese
134:Dzongkha
99:Gurmukhi
94:Gujarati
32:a series
30:Part of
846:History
737:numbers
572:Chuvash
490:Complex
280:Ancient
272:History
219:Hokkien
207:Chinese
152:Burmese
142:Tibetan
129:Kannada
109:Sinhala
84:Bengali
1077:
1047:
1019:
684:Hebrew
654:Coptic
567:Brahmi
552:Aegean
509:
493:
475:
462:
449:
312:Muisca
252:Tangut
229:Korean
212:Suzhou
124:Telugu
882:bulla
679:Greek
664:GeŹ½ez
622:Abjad
602:Roman
562:Aztec
557:Attic
472:Mixed
430:table
322:Quipu
307:Mayan
162:Khmer
114:Tamil
1075:ISBN
1045:ISBN
1017:ISBN
798:LXXX
327:Rumi
182:Thai
104:Odia
1104:GPL
359:By
167:Lao
1116::
1102:,
1033:;
971:^
942:^
912:.
836:IX
731:A
424:60
419:20
414:16
409:12
404:10
34:on
1106:)
1083:.
1053:.
1025:.
832:X
828:I
794:L
790:X
767:.
720:e
713:t
706:v
515:)
513:Ļ
511:(
502:)
499:i
497:2
495:(
481:)
477:(
468:)
464:(
455:)
453:1
451:(
432:)
428:(
399:8
394:6
389:5
384:4
379:3
374:2
24:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.