582:. In almost all cases with precisely the meaning described in this article, exceptions being: Ackermann function (writing out A(4, 2) is indeed very expansive :) ), Largest known prime (ditto), and List of paradoxes. That is not a coincidence. Whether or not "decimal expansion" is the "right" term, it is the most commonly used term for this. And no, I did not go around changing all these links — although I may have changed one or two and I indeed adapted this article in preparation for the move, which I expected to be a walk-over. Secondly, to me "3055" is the decimal representation of the number whose hexadecimal representation is "BEF". The use of the term "decimal representation" in the preceding sentence is what I believe to be the primary one. It is used in this sense in the articles
84:
74:
53:
393:
This is what represents them as numbers, rather than simply symbols. Not only this, but "representation" de-emphasizes the decimal system (unless prefixed with "decimal", of course) since one could have a "vingtesimal" representation, or a "binary" representation, and so on, all "representing" the same abstract number. "Expansion" makes it sound too much like the desired representation is waiting inside to spring out and make the number legitimate. Just my two cents.
22:
873:
definition that might not otherwise have. But the fact that the rest of the entry was not consistent with that (a reference to "the decimal expansion" instead of "a decimal expansion" appeared earlier) leads me to conclude that that was not the intent. My correction should make the entry make more sense to anyone reading it.
881:
I have two issues with the definition given here. The are, in my opinion, not that important. First, why are do we never point out that every real number has a decimal representation? Sure it is a bit easier to define for non-negative real numbers, and everything that is interesting to talk about
392:
I don't like this, however, since it only works if you compare decimals to fractions. The modern perspective is more abstract than either, and employing decimals in describing elements of the real field is precisely representing them in terms of arithmetic on numerical quantities, namely integers.
383:
I vote for "representation" also, but here's one way in which "expansion" could make sense: especially in the math that most people know, numbers come in two forms, namely fractions and decimals. The fraction is a compact notation that "stands in" for a division, while the decimal is somehow a
872:
While initially perfectly coherent, the way this was said was logically incoherent. In this case I would ask what do you mean by a special case. If anything it might allow the integers and real numbers with finite decimal expansions, which are both rational numbers, to be included in your
388:
operations, so to speak, and obtaining a canonical form for an expression. Thus it is with reducing fractions, which are not at all canonical for the purposes of arithmetic or comparison, to decimals, which are. The canonicity tends to rely upon increasingly redundant information, hence
678:
majority of cases they use "decimal expansion" to describe it. This is all a result of how the editors of these articles naturally used the terms, even with the bias towards using the terms that give you a meaningful link. I rest my case (unless someone dares to contradict me :) ).
902:… we are sort of implicitly implying everything should be written base 10. I think the definition would be better served if we summed over some finite number of negative indices. And later made a comment that for negative numbers it is typical to represent them by -a
747:
the article claims that "every real number except zero has two representations". Is this true? What are two decimal representations for 1/3? I am under the impression that this only holds for numbers that admit representations with finitely many nonzero terms.
792:
I think the uniqueness is already covered above with the wording "normalized representation". Anyway, I would suggest merging the two paragraphs into one, because as it is now, the repetition of the 999-000 argument is most striking.
353:
I guess the article uses "expaniòn" because it was changed in preparation of the move. I prefer "decimal expansion", seeing that the article only talks about infinite series sum_k a_k 10^(-k). But it's only a slight preference. --
423:, then I might have gone the other way. But given that this is aimed at a more sophisticated audience, I think "representation" conveys more accurately what this article is about. But really, I don't think it matters.
721:
is better, or a short informal article covering both integers and reals with appropriate "See further"s. But in any case, I can't do "what I like"; only a sysop can do this (see my post above and
402:
I tick the box called "representation" instinctively, and the argument that an "expansion" is a better term for a natural operation that doesn't require an arbitrary choice of base is a good one.
140:
696:
Hey lambiam, judging by the strength of the opinions expressed above, I think either title is okay, so do what you like. But I'm not sure that people would agree with making
869:
I reworded this entry from: "This happens precisely when the number is a rational number." - with a "special case" when the entry ends in infinite zeros (or nines).
438:
Lambiam speaking. For me, it is not so much a matter of what I like, but what is most useful. The term "decimal expansion" is used or linked to in several articles:
850:
I thought the expansion .999… is chosen for mere technical reasons. It certainly seems artificial to say that .999… is an infinite expansion while 1.000… is not.
670:. (Disclaimer: I used Google search; the articles may have changed.) So in the majority of cases where "decimal representation" is used, it means something
274:
exists. (Why isn't there a simple way of accomplishing the swapping a redirecting page and a redirected-to page not requiring the involvement of sysops?)
1021:
130:
1016:
539:
213:--I noticed the same thing until I looked closer and saw your correction. I think it might be clearest to rephrase it as: r == Sum from i=0:inf of a
106:
228:
953:
Isn't 1024 = 1*10^3+0*10^2+2*10^1+4*10^0 also the decimal representation of a real which is an integer? Why is a0 allowed to be : -->
659:
384:
terminal form which expands the fraction notation. "Expand", as a phrase used informally in mathematics, tends to mean eliminating
97:
58:
559:
982:, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
623:
499:
467:
344:. It's a bit jarring. Anyway, I favor decimal representation slightly, but my feelings on the matter are quite weak. -
33:
595:
459:
166:
can only take the values 0 through 9, and the least i is zero, then how (for example) is the value 42 represented?
603:
816:
780:
319:
200:
186:
829:(In haste) "normalized representation" handled above can be finite. This section is about infinite expansions.
232:
21:
221:
is an integer in . As it is I think you might be assuming that a non-negative integer looks a certain way.
758:
This comment is in response to an edit by mfc, which was subsequently fixed by
Dmharvey. So, nevermind. -
697:
639:
359:
333:
311:
286:
278:
264:
256:
244:
503:
39:
83:
812:
776:
315:
224:
196:
182:
954:
9 in contrast to the other digits? Shouldn't the integer part also be split up in decimal digits? —
939:
599:
551:
515:
105:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
647:
523:
475:
455:
451:
89:
851:
794:
73:
52:
993:
833:
728:
683:
619:
615:
611:
543:
527:
519:
511:
463:
355:
329:
300:
282:
271:
260:
248:
579:
563:
471:
447:
394:
181:
a_0=42, it does not have to be between 0 and 9, and 0<= a_i <= 9 for i=1, 2, ....
935:
759:
749:
705:
701:
667:
567:
555:
487:
373:
345:
290:
1010:
979:
959:
709:
607:
587:
583:
535:
531:
491:
479:
443:
424:
830:
725:
680:
571:
507:
297:
996:
962:
943:
854:
837:
820:
797:
784:
762:
752:
732:
712:
687:
427:
406:
397:
376:
363:
348:
323:
304:
236:
204:
190:
170:
314:, rather than "expansion", but don't have a good reason for why. Other comments?
1004:
Last edited at 21:30, 1 June 2007 (UTC). Substituted at 01:59, 5 May 2016 (UTC)
882:
happens in this case, but some comment should be made. Also the way we handle a
663:
591:
439:
403:
263:, since that name is the common way of referring to the topic described on page
102:
627:
79:
638:. It is used in the sense of decimal expansion representing a real number in
655:
635:
955:
631:
419:
I prefer "representation". If we didn't have the more accessible article
385:
167:
989:
718:
651:
495:
483:
420:
643:
575:
865:
Recurring decimal representations - some logical considerations
267:, as in "The decimal expansion of π is 3.14159265358979323..."
195:
You are right, it was confusing. I tried to clarify it a bit.
15:
886:
isn't perfect. When we make the correspondence with the r=a
372:
I like "representation". What are you expanding, exactly? --
547:
974:
722:
988:
Would be mid importance, but doesn't add so much to
101:, a collaborative effort to improve the coverage of
978:, and are posted here for posterity. Following
972:The comment(s) below were originally left at
8:
704:as you suggested above. Perhaps a "see also
336:, but then the article uses only the phrase
217:/ 10 where k is a non-negative integer and a
708:" entry on this article would work better.
328:The current state of the article is weird:
19:
47:
540:On-Line Encyclopedia of Integer Sequences
270:It can't be moved there because the page
674:described in this article, while in the
285:, it would then make sense to redirect
49:
775:(discussion started at my talk page.
7:
975:Talk:Decimal representation/Comments
95:This article is within the scope of
38:It is of interest to the following
14:
1022:Low-priority mathematics articles
980:several discussions in past years
660:Methods of computing square roots
115:Knowledge:WikiProject Mathematics
1017:Start-Class mathematics articles
809:Infinite decimal representations
805:Multiple decimal representations
743:infinite decimal representations
118:Template:WikiProject Mathematics
82:
72:
51:
20:
949:negative indices / integer part
624:Polymorphism (computer science)
281:have been replaced by links to
259:should more properly be called
135:This article has been rated as
934:… by our previous definition.
560:Proof that 22 over 7 exceeds π
1:
340:, and never defines the term
205:05:38, 24 February 2006 (UTC)
191:05:34, 24 February 2006 (UTC)
171:19:18, 23 February 2006 (UTC)
109:and see a list of open tasks.
944:09:14, 20 January 2009 (UTC)
468:Construction of real numbers
237:01:53, 28 January 2008 (UTC)
158:How to represent the answer?
963:15:52, 5 January 2014 (UTC)
717:Yes, perhaps a redirect to
1038:
855:09:23, 25 March 2006 (UTC)
838:22:19, 24 March 2006 (UTC)
821:17:28, 24 March 2006 (UTC)
811:need some kind of mergin.
798:16:18, 24 March 2006 (UTC)
785:17:28, 24 March 2006 (UTC)
763:20:02, 22 March 2006 (UTC)
753:20:00, 22 March 2006 (UTC)
733:16:00, 22 March 2006 (UTC)
713:15:28, 22 March 2006 (UTC)
688:14:52, 22 March 2006 (UTC)
604:Computer numbering formats
596:Cantor's diagonal argument
460:Cantor's diagonal argument
428:16:02, 21 March 2006 (UTC)
407:15:51, 21 March 2006 (UTC)
398:05:11, 21 March 2006 (UTC)
377:04:51, 21 March 2006 (UTC)
364:04:22, 21 March 2006 (UTC)
349:04:10, 21 March 2006 (UTC)
324:03:39, 21 March 2006 (UTC)
305:21:20, 20 March 2006 (UTC)
176:Well, it is 42.0000000....
987:
500:Fransén-Robinson constant
310:Heh. I seem to like more
134:
67:
46:
997:21:30, 1 June 2007 (UTC)
666:, and in both senses in
141:project's priority scale
98:WikiProject Mathematics
803:I agree. The sections
698:decimal representation
640:Bounded complete poset
342:decimal representation
334:decimal representation
312:decimal representation
287:Decimal representation
279:Decimal representation
265:Decimal representation
257:Decimal representation
245:Decimal representation
28:This article is rated
504:Forcing (mathematics)
769:Merging two sections
121:mathematics articles
552:Positional notation
516:Largest known prime
968:Assessment comment
648:Continued fraction
524:List of YTMND fads
476:Continued fraction
456:Adriaan van Roomen
452:Ackermann function
90:Mathematics portal
34:content assessment
1002:
1001:
835:
730:
685:
620:Markup (business)
616:Irrational number
612:Intel BCD opcodes
544:Periodic function
528:Logarithmic scale
520:List of paradoxes
512:Irrational number
464:Computable number
338:decimal expansion
330:decimal expansion
302:
283:Decimal expansion
272:Decimal expansion
261:Decimal expansion
249:Decimal expansion
239:
227:comment added by
155:
154:
151:
150:
147:
146:
1029:
985:
984:
977:
877:Annoying comment
834:
729:
684:
600:Colón (currency)
301:
222:
123:
122:
119:
116:
113:
92:
87:
86:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
1037:
1036:
1032:
1031:
1030:
1028:
1027:
1026:
1007:
1006:
973:
970:
951:
933:
929:
925:
921:
917:
913:
909:
905:
901:
897:
893:
889:
885:
879:
867:
813:Oleg Alexandrov
777:Oleg Alexandrov
771:
745:
580:Yasumasa Kanada
564:Rational number
472:Contact (novel)
448:142857 (number)
316:Oleg Alexandrov
277:After links to
252:
220:
216:
197:Oleg Alexandrov
183:Oleg Alexandrov
165:
160:
120:
117:
114:
111:
110:
88:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
1035:
1033:
1025:
1024:
1019:
1009:
1008:
1000:
999:
969:
966:
950:
947:
931:
927:
923:
919:
915:
911:
907:
903:
899:
895:
891:
887:
883:
878:
875:
866:
863:
862:
861:
860:
859:
858:
857:
843:
842:
841:
840:
824:
823:
790:
789:
770:
767:
766:
765:
744:
741:
740:
739:
738:
737:
736:
735:
706:numeral system
702:numeral system
691:
690:
668:Numeral system
568:Regular number
556:Prime constant
435:
434:
433:
432:
431:
430:
412:
411:
410:
409:
390:
380:
379:
370:
369:
368:
367:
366:
295:
294:
291:Numeral system
275:
268:
251:
241:
229:74.139.216.101
218:
214:
212:
210:
209:
208:
207:
178:
177:
163:
159:
156:
153:
152:
149:
148:
145:
144:
133:
127:
126:
124:
107:the discussion
94:
93:
77:
65:
64:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
1034:
1023:
1020:
1018:
1015:
1014:
1012:
1005:
998:
995:
991:
986:
983:
981:
976:
967:
965:
964:
961:
957:
948:
946:
945:
941:
937:
876:
874:
870:
864:
856:
853:
849:
848:
847:
846:
845:
844:
839:
836:
832:
828:
827:
826:
825:
822:
818:
814:
810:
806:
802:
801:
800:
799:
796:
788:
786:
782:
778:
773:
772:
768:
764:
761:
757:
756:
755:
754:
751:
742:
734:
731:
727:
723:
720:
716:
715:
714:
711:
707:
703:
699:
695:
694:
693:
692:
689:
686:
682:
677:
673:
669:
665:
661:
657:
653:
649:
645:
641:
637:
633:
629:
625:
621:
617:
613:
609:
608:DRTE Computer
605:
601:
597:
593:
589:
588:1729 (number)
585:
584:1000 (number)
581:
577:
573:
569:
565:
561:
557:
553:
549:
545:
541:
537:
536:Normal number
533:
532:Long division
529:
525:
521:
517:
513:
509:
505:
501:
497:
493:
492:Feynman point
489:
485:
481:
480:Countable set
477:
473:
469:
465:
461:
457:
453:
449:
445:
444:1000 (number)
441:
437:
436:
429:
426:
422:
418:
417:
416:
415:
414:
413:
408:
405:
401:
400:
399:
396:
391:
387:
382:
381:
378:
375:
371:
365:
361:
357:
352:
351:
350:
347:
343:
339:
335:
332:redirects to
331:
327:
326:
325:
321:
317:
313:
309:
308:
307:
306:
303:
299:
292:
288:
284:
280:
276:
273:
269:
266:
262:
258:
254:
253:
250:
246:
242:
240:
238:
234:
230:
226:
206:
202:
198:
194:
193:
192:
188:
184:
180:
179:
175:
174:
173:
172:
169:
157:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
1003:
994:Geometry guy
971:
952:
880:
871:
868:
808:
804:
791:
774:
746:
700:redirect to
676:overwhelming
675:
671:
572:Unique prime
508:Golden ratio
356:Jitse Niesen
341:
337:
296:
211:
161:
137:Low-priority
136:
96:
62:Low‑priority
40:WikiProjects
918:where |r|=a
664:Real number
592:53 (number)
488:Digits of π
440:19 (number)
223:—Preceding
112:Mathematics
103:mathematics
59:Mathematics
30:Start-class
1011:Categories
628:Sexy prime
395:Ryan Reich
389:expansion.
936:Thenub314
656:Enneagram
636:Unix time
374:Trovatore
255:The page
243:Renaming
710:Dmharvey
632:Trigraph
425:Dmharvey
386:immanent
225:unsigned
990:Decimal
831:Lambiam
726:Lambiam
719:Decimal
681:Lambiam
652:Decimal
634:, and
496:Fractal
484:Decimal
421:decimal
298:Lambiam
139:on the
662:, and
578:, and
404:Elroch
36:scale.
852:Hylas
795:Hylas
760:lethe
750:lethe
644:Bzip2
346:lethe
960:Talk
940:talk
817:talk
807:and
781:talk
576:Week
360:talk
320:talk
233:talk
201:talk
187:talk
162:If a
956:MFH
724:).
672:not
289:to
247:to
168:mfc
131:Low
1013::
992:.
942:)
922:.a
906:.a
890:.a
819:)
783:)
658:,
654:,
650:,
646:,
642:,
630:,
626:,
622:,
618:,
614:,
610:,
606:,
602:,
598:,
594:,
590:,
586:,
574:,
570:,
566:,
562:,
558:,
554:,
550:,
548:Pi
546:,
542:,
538:,
534:,
530:,
526:,
522:,
518:,
514:,
510:,
506:,
502:,
498:,
494:,
490:,
486:,
482:,
478:,
474:,
470:,
466:,
462:,
458:,
454:,
450:,
446:,
442:,
362:)
322:)
235:)
203:)
189:)
958::
938:(
932:3
930:a
928:2
926:a
924:1
920:0
916:3
914:a
912:2
910:a
908:1
904:0
900:3
898:a
896:2
894:a
892:1
888:0
884:0
815:(
787:)
779:(
748:-
358:(
318:(
293:.
231:(
219:i
215:i
199:(
185:(
164:i
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
