1085:
s are obviously linearly independent and they are in the center, so they form a basis. The proof is kind of obvious if you've been working with these sums long enough, but probably not if you never seen them before. My group theory book (W.R. Scott) gives the proof in 7 lines, slightly different than
620:
If we know f(n)=(1/n^2) for all integers n, and f is analytic in the complex plane except for possibly at some singularities, then what more would we need to know in order to establish g exactly? Obviously you could have g(z)=cos(2piz)/(z^2) or something similar so it needn't necessarily be
456:. However, it's not really defined like that, it's a primitive notion: you are given a set of worlds, an accessibility relation, and truth values of atomic statements in each world, and all this together determines the truth values of compound statements (which may involve the
1215:(ec)Variables are useful here. When you want to manipulate some number, but you don't know what the number is, place a variable in its stead; this gives you information about the variable which later may allow you to determine its value.
1226:. How much did the 65 cents stamps she purchased cost? How many 50 cent stamps did she purchase? How much did they cost? What is the total cost (before tax) of all the stamps she purchased? How much did she spend (after tax)?
621:
g(z)=1/z^2 at this point - but I can't see how we can classify all possible g which take the appropriate values at integers, in order to work out what more information we need to know to identify g. Could anyone suggest anything?
1121:
Arriana bought two kinds of stamps, 50cent stamps, and 65cent stamps. She bought 40% more 50cent stamps then 65 cent stamps, spending a total of $ 50.56. How many of each type did she buy? There is a 7% tax on stamp sales.
66:
45:
936:
55:
51:
1400:
Indeed I must admit I was wondering why they couldn't just ask
Arriana or look at the stamps, and why did they want to know anyway? Surely you'd only want to know how any stamps you've got left.
59:
444:". You can ask whether a statement (formula) is possible in a world, but there is no concept of a world being possible in another world. The intuitive meaning of the accessibility relation
783:), but I can't seem to string it altogether. The notes I'm working with only dedicate one line to the explanation, so I feel I'm missing something pretty obvious. Thanks, as always!
1007:
1071:
841:
769:
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161:
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25:
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272:
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181:
129:
85:
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
671:(assuming that's what you mean by "analytic except for possibly at some singularities") which vanishes in all integer points. You can thus ignore the 1/
37:
586:⊨ is read 'models' rather than 'is', where models here means the right hand side proposition is true for the world given by the left hand side.
1242:
1132:
421:
21:
1229:
You know that the answer to the last question is $ 50.56 from the problem statement. Once you've answered the last question in terms of
1377:
625:
1409:
1385:
1250:
1208:
1140:
1102:
792:
717:? I've tried it out for a few concrete examples, and it worked, but I can't really see why. The closest I could come was taking
686:
633:
607:
573:
429:
852:
598:
as implementing the most common system, what the article calls the strongest logic S5, but this isn't necessarily so.
86:
17:
775:
has an inverse in the algebra. I know also that the class sums are invariant under conjugation by the elements of
1296:
after she left and found out that the total number of guests receiving invitations happens to be the same as the
1246:
1136:
425:
1381:
1128:
417:
558:
or not. The accessibility relation can be an arbitrary binary relation, in general it does not have to be
955:
1199:
instead of the actual amounts in each of the other statements as well and you've got some equations.
629:
1312:
1308:
698:
559:
1222:
be the number of 65 cent stamps that she bought. Then answer the following questions in terms of
1037:
807:
1281:
563:
732:
530:
342:
1147:
Start by giving a name to everything you dont know. these are called variable for some reason
1098:
788:
479:
134:
1369:
1264:
will suffice. (I suppose that's what you get when you ask such a question in a mathematics
583:
497:
1115:
Yes- I realize you won't help me with my homework, but I have no idea where to start here.
503:
299:
683:
570:
459:
675:
part, and concentrate on the (less messy, if not really easier) task of classifying such
368:
186:
1405:
1265:
1204:
603:
1340:
1317:
397:
322:
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232:
212:
166:
114:
1362:
1285:
1373:
1301:
1094:
784:
1357:. Moreover, the number of guests who lived locally, and not over the border in
1277:
1257:
594:
is a world. I think your business about inclusion is where you are thinking of
1261:
706:
680:
567:
1401:
1293:
1273:
1200:
599:
74:
500:. Your example does not make much sense as is, but even if we read it as "
1304:
1289:
1365:
1334:
1297:
414:
is like an equality relation, or a kind of "is a subset of" relation?
1358:
1269:
942:
where the second sum is obtained by reindexing the first one. But
79:
Welcome to the
Knowledge (XXG) Mathematics Reference Desk Archives
566:, hence neither equality nor "subset of" is an adequate analogy.—
1233:(using your previous answers), you will have an equation for
1260:
is the only way to solve these problems, when sometimes the
616:
What more do we need to know in order to
Identify a function
1164:
and then write them in like 40% more 50c stamps means take
108:
From the article, just trying to understand the semantics.
931:{\displaystyle z^{h}=\sum z_{g}g^{h}=\sum z_{g^{h^{-1}}}g}
771:, which introduces conjugation, but that's only true when
554:", this is insufficient information to determine whether
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1320:
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735:
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117:
1284:, and she crossed a name off her list as she put a
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123:
448:is actually that every statement that is true in
802:be in the center of the group algebra and write
1077:where the sum runs over the conjugacy classes
798:I think you're over thinking the problem. Let
163:are worlds. We have a accessibility relation
8:
1241:and solve the problem from there. Eric.
1342:
1319:
1276:work will do. I followed Arriana to the
1054:
1039:
986:
981:
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963:
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912:
907:
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824:
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746:
734:
532:
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481:
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344:
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259:
234:
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188:
168:
136:
116:
1093:A-hah, I see now - thanks for the help.
49:
36:
1024:depends only on the conjugacy class of
65:
43:
7:
1237:. This will allow you to calculate
1002:{\displaystyle z_{g}=z_{g^{h^{-1}}}}
705:, form a basis of the center of the
436:It does not make sense to say that "
1118:Can someone give me the equations?
32:
1292:. I pulled that list out of the
111:We have a non-empty set (frame)
1376:of the total number of guests.
1361:(and thus requiring the higher
1272:, ...) In this case a little
1017:. In other words the value of
667:is a function meromorphic in
18:Knowledge (XXG):Reference desk
1:
1410:12:00, 23 February 2010 (UTC)
1386:01:50, 23 February 2010 (UTC)
1251:22:11, 22 February 2010 (UTC)
1209:22:07, 22 February 2010 (UTC)
1191:All you do is write down the
1141:21:55, 22 February 2010 (UTC)
1103:21:37, 22 February 2010 (UTC)
1066:{\displaystyle z=\sum z_{C}C}
836:{\displaystyle z=\sum z_{g}g}
793:18:02, 22 February 2010 (UTC)
687:14:59, 22 February 2010 (UTC)
634:13:34, 22 February 2010 (UTC)
608:15:16, 22 February 2010 (UTC)
574:14:52, 22 February 2010 (UTC)
430:10:29, 22 February 2010 (UTC)
33:
1268:. When your only tool is a
1159:for the number of 65c stamps
1153:for the number of 50c stamps
779:(i.e. the basis elements of
721:to be in the centre - then
1431:
764:{\displaystyle h=z^{-1}hz}
543:{\displaystyle \Diamond p}
355:{\displaystyle \Diamond p}
950:so matching coefficients
693:Centre of a group algebra
489:{\displaystyle \Diamond }
1280:when she mailed off her
156:{\displaystyle v,w\in G}
1351:
1328:
1067:
1003:
932:
837:
765:
624:Thanks all very much!
544:
517:
516:{\displaystyle \Box p}
490:
470:
408:
385:
356:
333:
313:
312:{\displaystyle \Box p}
290:
268:
243:
223:
203:
177:
157:
125:
87:current reference desk
1352:
1329:
1068:
1004:
933:
838:
766:
590:is a proposition and
545:
518:
491:
471:
469:{\displaystyle \Box }
409:
386:
357:
334:
314:
291:
269:
244:
224:
204:
178:
158:
126:
1341:
1318:
1256:Everyone acts as if
1125:Thanks in advance.
1038:
956:
853:
808:
733:
699:conjugacy class sums
531:
504:
480:
460:
398:
369:
343:
323:
300:
280:
258:
233:
213:
187:
167:
135:
115:
1309:mapping class group
1282:wedding invitations
729:in the algebra, so
384:{\displaystyle vRw}
202:{\displaystyle vRw}
1347:
1324:
1081:of the group. The
1063:
999:
928:
833:
761:
639:Your condition on
540:
513:
486:
466:
404:
381:
352:
329:
309:
286:
264:
239:
219:
199:
173:
153:
121:
1412:
1388:
1350:{\displaystyle g}
1327:{\displaystyle g}
1131:comment added by
713:, for some field
643:is equivalent to
420:comment added by
407:{\displaystyle R}
332:{\displaystyle v}
289:{\displaystyle w}
267:{\displaystyle p}
242:{\displaystyle w}
222:{\displaystyle v}
176:{\displaystyle R}
124:{\displaystyle G}
93:
92:
73:
72:
1422:
1399:
1356:
1354:
1353:
1348:
1333:
1331:
1330:
1325:
1255:
1143:
1072:
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993:
968:
967:
937:
935:
934:
929:
924:
923:
922:
921:
920:
919:
891:
890:
881:
880:
865:
864:
842:
840:
839:
834:
829:
828:
770:
768:
767:
762:
754:
753:
584:double turnstile
549:
547:
546:
541:
522:
520:
519:
514:
498:Kripke semantics
496:operators), see
495:
493:
492:
487:
475:
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467:
432:
413:
411:
410:
405:
390:
388:
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359:
358:
353:
338:
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318:
316:
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310:
295:
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287:
274:= it is snowing
273:
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248:
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228:
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162:
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130:
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122:
75:
38:Mathematics desk
34:
1430:
1429:
1425:
1424:
1423:
1421:
1420:
1419:
1372:of the largest
1339:
1338:
1316:
1315:
1300:of the largest
1243:131.215.159.171
1126:
1113:
1050:
1036:
1035:
1032:can be written
1022:
982:
977:
972:
959:
954:
953:
908:
903:
898:
882:
872:
856:
851:
850:
820:
806:
805:
742:
731:
730:
695:
618:
529:
528:
502:
501:
478:
477:
458:
457:
452:is possible in
440:is possible in
415:
396:
395:
394:Does this mean
367:
366:
341:
340:
321:
320:
298:
297:
278:
277:
256:
255:
252:As an example:
231:
230:
229:is possible in
211:
210:
185:
184:
165:
164:
133:
132:
113:
112:
106:
101:
30:
29:
28:
12:
11:
5:
1428:
1426:
1418:
1417:
1416:
1415:
1414:
1413:
1392:
1391:
1390:
1389:
1346:
1323:
1227:
1216:
1212:
1211:
1189:
1188:
1187:
1162:
1161:
1160:
1154:
1133:174.112.38.185
1112:
1109:
1108:
1107:
1106:
1105:
1088:
1087:
1075:
1074:
1073:
1062:
1057:
1053:
1049:
1046:
1043:
1020:
1011:
1010:
1009:
992:
989:
985:
980:
975:
971:
966:
962:
940:
939:
938:
927:
918:
915:
911:
906:
901:
897:
894:
889:
885:
879:
875:
871:
868:
863:
859:
845:
844:
843:
832:
827:
823:
819:
816:
813:
760:
757:
752:
749:
745:
741:
738:
694:
691:
690:
689:
617:
614:
613:
612:
611:
610:
577:
576:
539:
536:
512:
509:
485:
465:
422:81.149.255.225
403:
380:
377:
374:
351:
348:
328:
308:
305:
285:
263:
238:
218:
198:
195:
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100:
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95:
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82:
81:
71:
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64:
48:
41:
40:
31:
15:
14:
13:
10:
9:
6:
4:
3:
2:
1427:
1411:
1407:
1403:
1398:
1397:
1396:
1395:
1394:
1393:
1387:
1383:
1379:
1378:58.147.60.130
1375:
1371:
1367:
1364:
1363:international
1360:
1344:
1336:
1321:
1314:
1310:
1306:
1303:
1299:
1295:
1291:
1287:
1283:
1279:
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1267:
1263:
1259:
1254:
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1244:
1240:
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1228:
1225:
1221:
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1213:
1210:
1206:
1202:
1198:
1194:
1190:
1186:
1182:
1178:
1177:
1175:
1171:
1167:
1163:
1158:
1155:
1152:
1149:
1148:
1146:
1145:
1144:
1142:
1138:
1134:
1130:
1123:
1119:
1116:
1110:
1104:
1100:
1096:
1092:
1091:
1090:
1089:
1086:the one here.
1084:
1080:
1076:
1060:
1055:
1051:
1047:
1044:
1041:
1034:
1033:
1031:
1027:
1023:
1016:
1012:
990:
987:
983:
978:
973:
969:
964:
960:
952:
951:
949:
945:
941:
925:
916:
913:
909:
904:
899:
895:
892:
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883:
877:
873:
869:
866:
861:
857:
849:
848:
846:
830:
825:
821:
817:
814:
811:
804:
803:
801:
797:
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795:
794:
790:
786:
782:
778:
774:
758:
755:
750:
747:
743:
739:
736:
728:
724:
720:
716:
712:
708:
707:group algebra
704:
700:
692:
688:
685:
682:
678:
674:
670:
666:
662:
658:
654:
650:
646:
642:
638:
637:
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635:
631:
627:
622:
615:
609:
605:
601:
597:
593:
589:
585:
581:
580:
579:
578:
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572:
569:
565:
561:
557:
553:
537:
534:
526:
510:
507:
499:
483:
463:
455:
451:
447:
443:
439:
435:
434:
433:
431:
427:
423:
419:
401:
392:
378:
375:
372:
363:
349:
346:
326:
306:
303:
283:
275:
261:
253:
250:
236:
216:
196:
193:
190:
170:
150:
147:
144:
141:
138:
118:
109:
103:
98:
96:
88:
84:
83:
80:
77:
76:
68:
61:
57:
53:
47:
42:
39:
35:
27:
23:
19:
1374:prime factor
1238:
1234:
1230:
1223:
1219:
1196:
1192:
1184:
1180:
1179:(1 + 40/100)
1173:
1172:and you get
1169:
1165:
1156:
1150:
1124:
1120:
1117:
1114:
1082:
1078:
1029:
1025:
1018:
1014:
947:
943:
799:
780:
776:
772:
726:
722:
718:
714:
710:
702:
701:of a group,
696:
676:
672:
668:
664:
660:
656:
652:
648:
644:
640:
623:
619:
595:
591:
587:
555:
551:
524:
453:
449:
445:
441:
437:
393:
364:
276:
254:
251:
183:, such that
110:
107:
94:
78:
1368:), was the
1337:divided by
1278:post office
1258:mathematics
1176:or shorter
1168:and 40% of
1127:—Preceding
697:Why do the
550:is true in
523:is true in
416:—Preceding
209:means that
104:Modal logic
99:February 22
67:February 23
46:February 21
26:Mathematics
1262:humanities
626:82.6.96.22
560:transitive
365:Therefore
1274:detective
1111:Math Help
663:), where
564:reflexive
50:<<
1305:subgroup
1290:envelope
1288:on each
1129:unsigned
1013:for all
946:for all
725:for all
418:unsigned
56:February
24: |
22:Archives
20: |
1366:postage
1335:surface
1307:of the
1298:lim sup
1095:Icthyos
785:Icthyos
723:hz = zh
89:pages.
1370:square
1359:Canada
1302:finite
1270:hammer
651:) = 1/
131:, and
1313:genus
1311:of a
1294:trash
1286:stamp
1266:forum
1028:. So
847:Then
556:v R w
446:v R w
69:: -->
63:: -->
62:: -->
44:<
16:<
1406:talk
1402:Dmcq
1382:talk
1247:talk
1218:Let
1205:talk
1201:Dmcq
1137:talk
1099:talk
789:talk
681:Emil
630:talk
604:talk
600:Dmcq
582:The
568:Emil
527:and
476:and
426:talk
944:z=z
562:or
339:is
296:is
60:Mar
52:Jan
1408:)
1384:)
1249:)
1207:)
1195:or
1183:=
1139:)
1101:)
1048:∑
988:−
914:−
896:∑
870:∑
818:∑
791:)
781:FG
748:−
711:FG
709:,
684:J.
679:.—
655:+
632:)
606:)
571:J.
535:◊
508:◻
484:◊
464:◻
428:)
391:.
362:.
347:◊
319:.
304:◻
249:.
148:∈
58:|
54:|
1404:(
1380:(
1345:g
1322:g
1245:(
1239:x
1235:x
1231:x
1224:x
1220:x
1203:(
1197:y
1193:x
1185:x
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1170:y
1166:y
1157:y
1151:x
1135:(
1097:(
1083:C
1079:C
1061:C
1056:C
1052:z
1045:=
1042:z
1030:z
1026:g
1021:g
1019:z
1015:h
991:1
984:h
979:g
974:z
970:=
965:g
961:z
948:h
926:g
917:1
910:h
905:g
900:z
893:=
888:h
884:g
878:g
874:z
867:=
862:h
858:z
831:g
826:g
822:z
815:=
812:z
800:z
787:(
777:G
773:z
759:z
756:h
751:1
744:z
740:=
737:h
727:z
719:h
715:F
703:G
677:h
673:z
669:C
665:h
661:z
659:(
657:h
653:z
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592:w
588:p
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379:w
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373:v
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327:v
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284:w
262:p
237:w
217:v
197:w
194:R
191:v
171:R
151:G
145:w
142:,
139:v
119:G
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