209:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000 Demostración :@0.108233:0.096657:0.224306:0.096657:0.224306:0.079711:0.108233:0.079711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean = ( , , ), = ( , , ), = ( , , ) tres elemen-:@0.217525:0.096194:0.595817:0.096194:0.595817:0.079697:0.217525:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.261257:0.096310:0.270466:0.096310:0.270466:0.079841:0.261257:0.079841:0.000000 :@0.264205:0.096686:0.270620:0.096686:0.270620:0.080868:0.264205:0.080868:0.000000 a b c v:@0.294817:0.096310:0.353403:0.096310:0.353403:0.079841:0.294817:0.079841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.347623:0.096686:0.354038:0.096686:0.354038:0.080868:0.347623:0.080868:0.000000 x y z w:@0.378236:0.096310:0.437630:0.096310:0.437630:0.079841:0.378236:0.079841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.429924:0.096686:0.436340:0.096686:0.436340:0.080868:0.429924:0.080868:0.000000 p q r:@0.461500:0.096310:0.498913:0.096310:0.498913:0.079841:0.461500:0.079841:0.000000:0.000000:0.000000:0.000000:0.000000 tos arbitrarios de .:@0.108291:0.113545:0.252831:0.113545:0.252831:0.097047:0.108291:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.231819:0.112458:0.245124:0.112458:0.245124:0.099596:0.231819:0.099596:0.000000 3:@0.245122:0.107193:0.250075:0.107193:0.250075:0.097575:0.245122:0.097575:0.000000 i.:@0.108226:0.145441:0.115835:0.145441:0.115835:0.128727:0.108226:0.128727:0.000000:0.000000 :@0.115835:0.145225:0.119977:0.145225:0.119977:0.128728:0.115835:0.128728:0.000000 Conmutativa :@0.131959:0.145442:0.236493:0.145442:0.236493:0.128728:0.131959:0.128728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . De la definición de suma de elementos en :@0.229654:0.145225:0.554753:0.145225:0.554753:0.128728:0.229654:0.128728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.556782:0.144142:0.570087:0.144142:0.570087:0.131280:0.556782:0.131280:0.000000 3:@0.570085:0.138877:0.575038:0.138877:0.575038:0.129259:0.570085:0.129259:0.000000 se :@0.575039:0.145229:0.599910:0.145229:0.599910:0.128731:0.575039:0.128731:0.000000:0.000000:0.000000:0.000000 tiene + = ( , , ) + ( , , ) = ( + , + , + ).:@0.131976:0.162580:0.501580:0.162580:0.501580:0.146082:0.131976:0.146082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.175824:0.162695:0.212062:0.162695:0.212062:0.146227:0.175824:0.146227:0.000000:0.000000:0.000000 :@0.178772:0.163071:0.185187:0.163071:0.185187:0.147253:0.178772:0.147253:0.000000 :@0.206282:0.163071:0.212698:0.163071:0.212698:0.147253:0.206282:0.147253:0.000000 a b c:@0.237742:0.162695:0.276967:0.162695:0.276967:0.146227:0.237742:0.146227:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.307964:0.162695:0.343567:0.162695:0.343567:0.146227:0.307964:0.146227:0.000000:0.000000:0.000000:0.000000:0.000000 a x b y c z:@0.374564:0.162695:0.492872:0.162695:0.492872:0.146227:0.374564:0.146227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Además, + = ( , , ) + ( , , ) = ( + , + , + ),:@0.131976:0.179930:0.523466:0.179930:0.523466:0.163433:0.131976:0.163433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.197709:0.180046:0.205492:0.180046:0.205492:0.163577:0.197709:0.163577:0.000000 :@0.199713:0.180422:0.206128:0.180422:0.206128:0.164604:0.199713:0.164604:0.000000 u:@0.225220:0.180046:0.234429:0.180046:0.234429:0.163577:0.225220:0.163577:0.000000 :@0.228168:0.180422:0.234583:0.180422:0.234583:0.164604:0.228168:0.164604:0.000000 x y z:@0.259628:0.180046:0.295230:0.180046:0.295230:0.163577:0.259628:0.163577:0.000000:0.000000:0.000000:0.000000:0.000000 a b c:@0.326228:0.180046:0.365452:0.180046:0.365452:0.163577:0.326228:0.163577:0.000000:0.000000:0.000000:0.000000:0.000000 x a y b z c:@0.396450:0.180046:0.514758:0.180046:0.514758:0.163577:0.396450:0.163577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y por la propiedad conmutativa de la operación adición “+” en , :@0.108241:0.197281:0.599909:0.197281:0.599909:0.180784:0.108241:0.180784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.579709:0.196194:0.593014:0.196194:0.593014:0.183332:0.579709:0.183332:0.000000 obtenemos + = ( + , + , + ). Por la definición de igual-:@0.131975:0.214632:0.595727:0.214632:0.595727:0.198134:0.131975:0.198134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.217667:0.214748:0.225450:0.214748:0.225450:0.198279:0.217667:0.198279:0.000000 :@0.219671:0.215124:0.226086:0.215124:0.226086:0.199305:0.219671:0.199305:0.000000 u:@0.245756:0.214748:0.254965:0.214748:0.254965:0.198279:0.245756:0.198279:0.000000 :@0.248723:0.215124:0.255138:0.215124:0.255138:0.199305:0.248723:0.199305:0.000000 a:@0.280761:0.214748:0.289739:0.214748:0.289739:0.198279:0.280761:0.198279:0.000000 x b:@0.309408:0.214748:0.333374:0.214748:0.333374:0.198279:0.309408:0.198279:0.000000:0.000000:0.000000 y c:@0.353044:0.214748:0.375122:0.214748:0.375122:0.198279:0.353044:0.198279:0.000000:0.000000:0.000000 z:@0.394792:0.214748:0.401439:0.214748:0.401439:0.198279:0.394792:0.198279:0.000000 dad de elementos en se tiene::@0.131975:0.231983:0.364478:0.231983:0.364478:0.215485:0.131975:0.215485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.285056:0.230896:0.298361:0.230896:0.298361:0.218034:0.285056:0.218034:0.000000 3:@0.298361:0.225631:0.303314:0.225631:0.303314:0.216013:0.298361:0.216013:0.000000 :@0.108234:0.249333:0.112376:0.249333:0.112376:0.232836:0.108234:0.232836:0.000000 u v:@0.241433:0.249449:0.277671:0.249449:0.277671:0.232980:0.241433:0.232980:0.000000:0.000000:0.000000 :@0.244381:0.249825:0.250796:0.249825:0.250796:0.234007:0.244381:0.234007:0.000000 + = + = ( + , + , + ).:@0.250796:0.249333:0.486333:0.249333:0.486333:0.232836:0.250796:0.232836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.271891:0.249825:0.278307:0.249825:0.278307:0.234007:0.271891:0.234007:0.000000 v:@0.297399:0.249449:0.305182:0.249449:0.305182:0.232980:0.297399:0.232980:0.000000 :@0.299402:0.249825:0.305818:0.249825:0.305818:0.234007:0.299402:0.234007:0.000000 u:@0.324909:0.249449:0.334118:0.249449:0.334118:0.232980:0.324909:0.232980:0.000000 :@0.327857:0.249825:0.334272:0.249825:0.334272:0.234007:0.327857:0.234007:0.000000 a x b y c z:@0.359317:0.249449:0.477625:0.249449:0.477625:0.232980:0.359317:0.232980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Conclusión: + = + .:@0.131988:0.266684:0.315220:0.266684:0.315220:0.250187:0.131988:0.250187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.219626:0.266800:0.255864:0.266800:0.255864:0.250331:0.219626:0.250331:0.000000:0.000000:0.000000 :@0.222573:0.267176:0.228989:0.267176:0.228989:0.251358:0.222573:0.251358:0.000000 :@0.250084:0.267176:0.256499:0.267176:0.256499:0.251358:0.250084:0.251358:0.000000 v:@0.275591:0.266800:0.283374:0.266800:0.283374:0.250331:0.275591:0.250331:0.000000 :@0.277595:0.267176:0.284010:0.267176:0.284010:0.251358:0.277595:0.251358:0.000000 u:@0.303102:0.266800:0.312311:0.266800:0.312311:0.250331:0.303102:0.250331:0.000000 :@0.306050:0.267176:0.312465:0.267176:0.312465:0.251358:0.306050:0.251358:0.000000 ii. :@0.108253:0.298581:0.124205:0.298581:0.124205:0.281867:0.108253:0.281866:0.000000:0.000000:0.000000:0.000000 Existencia del elemento neutro :@0.131988:0.298581:0.365926:0.298581:0.365926:0.281867:0.131988:0.281867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . El elemento 0 = (0, 0, 0) pertene-:@0.359087:0.298364:0.595780:0.298364:0.595780:0.281867:0.359087:0.281867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.454854:0.296340:0.465990:0.297598:0.465990:0.281780:0.454854:0.280522:0.000000:0.000000 ce a , donde 0 es el elemento neutro. Entonces,:@0.131988:0.315715:0.517216:0.315719:0.517216:0.299221:0.131988:0.299218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.163918:0.314632:0.177223:0.314632:0.177223:0.301770:0.163918:0.301770:0.000000 3:@0.177223:0.309367:0.182176:0.309367:0.182176:0.299749:0.177223:0.299749:0.000000 :@0.252743:0.315200:0.267395:0.315200:0.267395:0.301827:0.252743:0.301827:0.000000 R:@0.271242:0.314632:0.284547:0.314632:0.284547:0.301770:0.271242:0.301770:0.000000 :@0.108238:0.333070:0.112380:0.333070:0.112380:0.316572:0.108238:0.316572:0.000000 u:@0.131973:0.333185:0.141182:0.333185:0.141182:0.316717:0.131973:0.316717:0.000000 :@0.134920:0.333561:0.141336:0.333561:0.141336:0.317743:0.134920:0.317743:0.000000 + 0 = ( , , ) + (0, 0, 0) = ( + 0, + 0, + 0). Como + 0 = :@0.141336:0.333070:0.572531:0.333070:0.572531:0.316572:0.141336:0.316572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.161699:0.331045:0.168114:0.331045:0.168114:0.315227:0.161699:0.315227:0.000000 a b c:@0.193063:0.333185:0.232287:0.333185:0.232287:0.316717:0.193063:0.316717:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.332890:0.333185:0.341868:0.333185:0.341868:0.316717:0.332890:0.316717:0.000000 b:@0.376353:0.333185:0.385619:0.333185:0.385619:0.316717:0.376353:0.316717:0.000000 c:@0.420104:0.333185:0.427290:0.333185:0.427290:0.316717:0.420104:0.316717:0.000000 a:@0.516873:0.333185:0.525851:0.333185:0.525851:0.316717:0.516873:0.316717:0.000000 a,:@0.572531:0.333185:0.584051:0.333185:0.584051:0.316717:0.572531:0.316717:0.000000:0.000000 :@0.108238:0.350420:0.112380:0.350420:0.112380:0.333923:0.108238:0.333923:0.000000 b:@0.131973:0.350536:0.141239:0.350536:0.141239:0.334067:0.131973:0.334067:0.000000 + 0 = + 0 = se sigue que::@0.141239:0.350420:0.360420:0.350420:0.360420:0.333923:0.141239:0.333923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b, c:@0.187919:0.350536:0.210941:0.350536:0.210941:0.334067:0.187919:0.334067:0.000000:0.000000:0.000000:0.000000 c,:@0.257621:0.350536:0.267812:0.350536:0.267812:0.334067:0.257621:0.334067:0.000000:0.000000 :@0.108238:0.367771:0.112380:0.367771:0.112380:0.351274:0.108238:0.351274:0.000000 u:@0.218646:0.367887:0.227855:0.367887:0.227855:0.351418:0.218646:0.351418:0.000000 :@0.221594:0.368263:0.228009:0.368263:0.228009:0.352445:0.221594:0.352445:0.000000 + 0 = ( + 0, + 0, + 0) = ( , , ) = .:@0.228009:0.367771:0.509109:0.367771:0.509109:0.351274:0.228009:0.351274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.248373:0.365747:0.254788:0.365747:0.254788:0.349929:0.248373:0.349929:0.000000 a:@0.279737:0.367887:0.288714:0.367887:0.288714:0.351418:0.279737:0.351418:0.000000 b:@0.323199:0.367887:0.332466:0.367887:0.332466:0.351418:0.323199:0.351418:0.000000 c:@0.366950:0.367887:0.374136:0.367887:0.374136:0.351418:0.366950:0.351418:0.000000 a b c:@0.432722:0.367887:0.471946:0.367887:0.471946:0.351418:0.432722:0.351418:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.496991:0.367887:0.506200:0.367887:0.506200:0.351418:0.496991:0.351418:0.000000 :@0.499938:0.368263:0.506354:0.368263:0.506354:0.352445:0.499938:0.352445:0.000000 :@0.108238:0.385122:0.112380:0.385122:0.112380:0.368624:0.108238:0.368624:0.000000 Conclusión: 0 es tal que para todo , + 0 = .:@0.131973:0.385122:0.542796:0.385122:0.542796:0.368624:0.131973:0.368624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.220882:0.383098:0.227297:0.383098:0.227297:0.367280:0.220882:0.367280:0.000000 :@0.231345:0.384603:0.245997:0.384603:0.245997:0.371230:0.231345:0.371230:0.000000 R:@0.249844:0.384035:0.263149:0.384035:0.263149:0.371173:0.249844:0.371173:0.000000 3:@0.263002:0.378770:0.267955:0.378770:0.267955:0.369152:0.263002:0.369152:0.000000 u:@0.418531:0.385238:0.427740:0.385238:0.427740:0.368769:0.418531:0.368769:0.000000 :@0.421480:0.385614:0.427896:0.385614:0.427896:0.369795:0.421480:0.369795:0.000000 :@0.432033:0.384603:0.446686:0.384603:0.446686:0.371230:0.432033:0.371230:0.000000 R:@0.450533:0.384035:0.463838:0.384035:0.463838:0.371173:0.450533:0.371173:0.000000 3:@0.463690:0.378770:0.468644:0.378770:0.468644:0.369152:0.463690:0.369152:0.000000 u:@0.475541:0.385238:0.484750:0.385238:0.484750:0.368769:0.475541:0.368769:0.000000 :@0.478489:0.385614:0.484904:0.385614:0.484904:0.369795:0.478489:0.369795:0.000000 :@0.505267:0.383098:0.511683:0.383098:0.511683:0.367280:0.505267:0.367280:0.000000 u:@0.530678:0.385238:0.539887:0.385238:0.539887:0.368769:0.530678:0.368769:0.000000 :@0.533626:0.385614:0.540041:0.385614:0.540041:0.369795:0.533626:0.369795:0.000000 iii. :@0.108230:0.417018:0.128438:0.417019:0.128438:0.400305:0.108230:0.400304:0.000000:0.000000:0.000000:0.000000:0.000000 Existencia de opuestos aditivos :@0.131964:0.417019:0.366712:0.417019:0.366712:0.400305:0.131964:0.400305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Dado = ( , , ) y como :@0.359872:0.416802:0.592820:0.416806:0.592820:0.400308:0.359872:0.400305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.410442:0.416918:0.419651:0.416918:0.419651:0.400449:0.410442:0.400449:0.000000 :@0.413391:0.417294:0.419807:0.417294:0.419807:0.401476:0.413391:0.401476:0.000000 a b c:@0.444852:0.416918:0.484076:0.416918:0.484076:0.400449:0.444852:0.400449:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.494175:0.416287:0.508827:0.416287:0.508827:0.402914:0.494175:0.402914:0.000000 R:@0.512674:0.415719:0.525979:0.415719:0.525979:0.402857:0.512674:0.402857:0.000000 3:@0.525832:0.410454:0.530785:0.410454:0.530785:0.400836:0.525832:0.400836:0.000000 a b c:@0.131975:0.434272:0.171199:0.434272:0.171199:0.417804:0.131975:0.417804:0.000000:0.000000:0.000000:0.000000:0.000000 , , , por la existencia de opuestos aditivos en , existen :@0.140953:0.434157:0.577155:0.434157:0.577155:0.417659:0.140953:0.417659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.175341:0.433638:0.189994:0.433638:0.189994:0.420265:0.175341:0.420265:0.000000 R:@0.193841:0.433070:0.207146:0.433070:0.207146:0.420208:0.193841:0.420208:0.000000 R:@0.503717:0.433070:0.517022:0.433070:0.517022:0.420208:0.503717:0.420208:0.000000 – , – , – , tales que +(– ) = 0, +(– ) = 0, +(– ) = 0. :@0.131974:0.451507:0.591956:0.451507:0.591956:0.435010:0.131974:0.435010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b c:@0.142473:0.451623:0.202696:0.451623:0.202696:0.435154:0.142473:0.435154:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.206841:0.450989:0.221493:0.450989:0.221493:0.437616:0.206841:0.437616:0.000000 R:@0.225339:0.450421:0.238644:0.450421:0.238644:0.437558:0.225339:0.437558:0.000000 a:@0.313149:0.451623:0.322127:0.451623:0.322127:0.435154:0.313149:0.435154:0.000000 a:@0.353529:0.451623:0.362507:0.451623:0.362507:0.435154:0.353529:0.435154:0.000000 b:@0.407087:0.451623:0.416353:0.451623:0.416353:0.435154:0.407087:0.435154:0.000000 b:@0.447756:0.451623:0.457022:0.451623:0.457022:0.435154:0.447756:0.435154:0.000000 c:@0.501602:0.451623:0.508788:0.451623:0.508788:0.435154:0.501602:0.435154:0.000000 c:@0.540190:0.451623:0.547376:0.451623:0.547376:0.435154:0.540190:0.435154:0.000000 Definimos = (– , – , – ) . Entonces,:@0.131979:0.468858:0.435734:0.468858:0.435734:0.452361:0.131979:0.452361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.209943:0.468974:0.217726:0.468974:0.217726:0.452505:0.209943:0.452505:0.000000 :@0.211949:0.469350:0.218364:0.469350:0.218364:0.453532:0.211949:0.453532:0.000000 a b c:@0.253909:0.468974:0.314132:0.468974:0.314132:0.452505:0.253909:0.452505:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.324220:0.468340:0.338873:0.468340:0.338873:0.454966:0.324220:0.454966:0.000000 R:@0.342720:0.467771:0.356024:0.467771:0.356024:0.454909:0.342720:0.454909:0.000000 3:@0.355877:0.462506:0.360830:0.462506:0.360830:0.452888:0.355877:0.452888:0.000000 :@0.108224:0.486209:0.112366:0.486209:0.112366:0.469711:0.108224:0.469711:0.000000 u v:@0.131959:0.486325:0.168197:0.486325:0.168197:0.469856:0.131959:0.469856:0.000000:0.000000:0.000000 :@0.134907:0.486701:0.141322:0.486701:0.141322:0.470882:0.134907:0.470882:0.000000 + = ( , , ) + (– , – , – ) = ( + (– ), + (– ), + (– )) = :@0.141322:0.486209:0.580012:0.486209:0.580012:0.469711:0.141322:0.469711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.162418:0.486701:0.168833:0.486701:0.168833:0.470882:0.162418:0.470882:0.000000 a b c:@0.193878:0.486325:0.233102:0.486325:0.233102:0.469856:0.193878:0.469856:0.000000:0.000000:0.000000:0.000000:0.000000 a b c:@0.274599:0.486325:0.334823:0.486325:0.334823:0.469856:0.274599:0.469856:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.365820:0.486325:0.374798:0.486325:0.374798:0.469856:0.365820:0.469856:0.000000 a b:@0.410342:0.486325:0.441437:0.486325:0.441437:0.469856:0.410342:0.469856:0.000000:0.000000:0.000000 b c:@0.476981:0.486325:0.506283:0.486325:0.506283:0.469856:0.476981:0.469856:0.000000:0.000000:0.000000 c:@0.541828:0.486325:0.549014:0.486325:0.549014:0.469856:0.541828:0.469856:0.000000 (0, 0, 0) = 0.:@0.131959:0.503560:0.211910:0.503560:0.211910:0.487062:0.131959:0.487062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.202836:0.501535:0.209252:0.501535:0.209252:0.485717:0.202836:0.485717:0.000000 :@0.108224:0.520910:0.112366:0.520910:0.112366:0.504413:0.108224:0.504413:0.000000 Conclusión: dado = ( , , ) , existe = (– , – , – ) , :@0.131959:0.520910:0.599911:0.520910:0.599911:0.504413:0.131959:0.504413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.261961:0.521026:0.271170:0.521026:0.271170:0.504557:0.261961:0.504557:0.000000 :@0.264928:0.521402:0.271344:0.521402:0.271344:0.505584:0.264928:0.505584:0.000000 a b c:@0.297660:0.521026:0.338175:0.521026:0.338175:0.504557:0.297660:0.504557:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.348928:0.520392:0.363581:0.520392:0.363581:0.507019:0.348928:0.507019:0.000000 R:@0.368071:0.519824:0.381376:0.519824:0.381376:0.506961:0.368071:0.506961:0.000000 3:@0.381228:0.514559:0.386182:0.514559:0.386182:0.504941:0.381228:0.504941:0.000000 v:@0.438254:0.521026:0.446038:0.521026:0.446038:0.504557:0.438254:0.504557:0.000000 :@0.440277:0.521402:0.446693:0.521402:0.446693:0.505584:0.440277:0.505584:0.000000 a b c:@0.483509:0.521026:0.545003:0.521026:0.545003:0.504557:0.483509:0.504557:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.555762:0.520392:0.570414:0.520392:0.570414:0.507019:0.555762:0.507019:0.000000 R:@0.574903:0.519824:0.588208:0.519824:0.588208:0.506961:0.574903:0.506961:0.000000 3:@0.588060:0.514559:0.593013:0.514559:0.593013:0.504941:0.588060:0.504941:0.000000 tal que + = 0.:@0.131977:0.538261:0.252481:0.538261:0.252481:0.521764:0.131977:0.521764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.185265:0.538377:0.221503:0.538377:0.221503:0.521908:0.185265:0.521908:0.000000:0.000000:0.000000 :@0.188212:0.538753:0.194628:0.538753:0.194628:0.522935:0.188212:0.522935:0.000000 :@0.215723:0.538753:0.222138:0.538753:0.222138:0.522935:0.215723:0.522935:0.000000 Ejercicios resueltos:@0.108242:0.573339:0.238897:0.573339:0.238897:0.556552:0.108242:0.556552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.108242:0.590530:0.120514:0.590530:0.120514:0.573816:0.108242:0.573816:0.000000:0.000000 El opuesto aditivo de = (0, –8, 10) es – = (0, 8, –10). Nota que :@0.120514:0.590314:0.594841:0.590314:0.594841:0.573816:0.120514:0.573816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.285711:0.590429:0.294920:0.590429:0.294920:0.573960:0.285711:0.573960:0.000000 :@0.288661:0.590805:0.295076:0.590805:0.295076:0.574987:0.288661:0.574987:0.000000 u:@0.417507:0.590429:0.426715:0.590429:0.426715:0.573960:0.417507:0.573960:0.000000 :@0.420454:0.590805:0.426870:0.590805:0.426870:0.574987:0.420454:0.574987:0.000000 :@0.108241:0.607664:0.112383:0.607664:0.112383:0.591167:0.108241:0.591167:0.000000 u:@0.131976:0.607780:0.141185:0.607780:0.141185:0.591311:0.131976:0.591311:0.000000 :@0.134924:0.608156:0.141339:0.608156:0.141339:0.592338:0.134924:0.592338:0.000000 + (– ) = (0, –8, 10) + (0, 8, –10) = (0 – 0, –8 + 8, 10 – 10) =:@0.141339:0.607664:0.565618:0.607664:0.565618:0.591167:0.141339:0.591167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.176884:0.607780:0.186092:0.607780:0.186092:0.591311:0.176884:0.591311:0.000000 :@0.179831:0.608156:0.186246:0.608156:0.186246:0.592338:0.179831:0.592338:0.000000 :@0.108241:0.625015:0.112383:0.625015:0.112383:0.608517:0.108241:0.608517:0.000000 (0, 0, 0) = 0.:@0.131976:0.625015:0.211927:0.625015:0.211927:0.608517:0.131976:0.608517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.202853:0.622991:0.209268:0.622991:0.209268:0.607173:0.202853:0.607173:0.000000 2.:@0.108241:0.656911:0.120513:0.656911:0.120513:0.640197:0.108241:0.640197:0.000000:0.000000 El opuesto aditivo de = –2, – , – es – = 2, , .:@0.120514:0.656695:0.558432:0.656695:0.558432:0.640198:0.120514:0.640198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.285711:0.656811:0.296981:0.656811:0.296981:0.640342:0.285711:0.640342:0.000000 :@0.288795:0.654671:0.295211:0.654671:0.295211:0.638853:0.288795:0.638853:0.000000 A:@0.450951:0.656811:0.462221:0.656811:0.462221:0.640342:0.450951:0.640342:0.000000 :@0.454034:0.654671:0.460449:0.654671:0.460449:0.638853:0.454034:0.638853:0.000000 :@0.108241:0.691397:0.112383:0.691397:0.112383:0.674899:0.108241:0.674899:0.000000 Se tiene + (– ) = –2, – , – + 2, , =:@0.131976:0.691397:0.482045:0.691397:0.482045:0.674899:0.131976:0.674899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.192161:0.691512:0.203431:0.691512:0.203431:0.675044:0.192161:0.675044:0.000000 :@0.195243:0.689372:0.201659:0.689372:0.201659:0.673554:0.195243:0.673554:0.000000 A:@0.237203:0.691512:0.248473:0.691512:0.248473:0.675044:0.237203:0.675044:0.000000 :@0.240285:0.689372:0.246701:0.689372:0.246701:0.673554:0.240285:0.673554:0.000000 :@0.108241:0.726098:0.112383:0.726098:0.112383:0.709601:0.108241:0.709601:0.000000 2 – 2, – + , – + = (0, 0, 0) = 0.:@0.131976:0.726098:0.425598:0.726098:0.425598:0.709601:0.131976:0.709601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.416524:0.724074:0.422939:0.724074:0.422939:0.708256:0.416524:0.708256:0.000000 :@0.108241:0.743449:0.112383:0.743449:0.112383:0.726951:0.108241:0.726951:0.000000 Resta en :@0.108234:0.762201:0.179697:0.762201:0.179697:0.744518:0.108234:0.744518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.179697:0.760707:0.194212:0.760707:0.194212:0.746676:0.179697:0.746676:0.000000 3:@0.194211:0.755371:0.199919:0.755371:0.199919:0.745062:0.194211:0.745062:0.000000 Definición :@0.108234:0.779371:0.195101:0.779371:0.195101:0.762425:0.108234:0.762425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean = ( , , ), = ( , , ) . Se define – como :@0.188319:0.778909:0.599903:0.778909:0.599903:0.762411:0.188319:0.762411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.233092:0.779024:0.242300:0.779024:0.242300:0.762556:0.233092:0.762556:0.000000 :@0.236039:0.779400:0.242455:0.779400:0.242455:0.763582:0.236039:0.763582:0.000000 a b c v:@0.267692:0.779024:0.327857:0.779024:0.327857:0.762556:0.267692:0.762556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.322078:0.779400:0.328493:0.779400:0.328493:0.763582:0.322078:0.763582:0.000000 x y z:@0.353731:0.779024:0.389545:0.779024:0.389545:0.762556:0.353731:0.762556:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.399747:0.778390:0.414399:0.778390:0.414399:0.765017:0.399747:0.765017:0.000000 R:@0.418347:0.777822:0.431651:0.777822:0.431651:0.764960:0.418347:0.764960:0.000000 3:@0.431504:0.772557:0.436457:0.772557:0.436457:0.762939:0.431504:0.762939:0.000000 u v:@0.512958:0.779024:0.549100:0.779024:0.549100:0.762556:0.512958:0.762556:0.000000:0.000000:0.000000 :@0.515925:0.779400:0.522341:0.779400:0.522341:0.763582:0.515925:0.763582:0.000000 :@0.543320:0.779400:0.549736:0.779400:0.549736:0.763582:0.543320:0.763582:0.000000 sigue: – = +(– ) = ( – , – , – ).:@0.108234:0.796259:0.412914:0.796259:0.412914:0.779762:0.108234:0.779762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.150983:0.796375:0.186913:0.796375:0.186913:0.779906:0.150983:0.779906:0.000000:0.000000:0.000000 :@0.153931:0.796751:0.160346:0.796751:0.160346:0.780933:0.153931:0.780933:0.000000 :@0.181134:0.796751:0.187549:0.796751:0.187549:0.780933:0.181134:0.780933:0.000000 u:@0.206641:0.796375:0.215850:0.796375:0.215850:0.779906:0.206641:0.779906:0.000000 :@0.209588:0.796751:0.216004:0.796751:0.216004:0.780933:0.209588:0.780933:0.000000 v:@0.247406:0.796375:0.255189:0.796375:0.255189:0.779906:0.247406:0.779906:0.000000 :@0.249410:0.796751:0.255825:0.796751:0.255825:0.780933:0.249410:0.780933:0.000000 a x b y c z:@0.286823:0.796375:0.404206:0.796375:0.404206:0.779906:0.286823:0.779906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Observa que el opuesto aditivo de = ( , , ) es:@0.108234:0.827939:0.490994:0.827943:0.490994:0.811446:0.108234:0.811441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.356713:0.828055:0.364496:0.828055:0.364496:0.811586:0.356713:0.811586:0.000000 :@0.358721:0.828431:0.365136:0.828431:0.365136:0.812612:0.358721:0.812612:0.000000 x y z:@0.390181:0.828055:0.425783:0.828055:0.425783:0.811586:0.390181:0.811586:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.435871:0.827425:0.450524:0.827425:0.450524:0.814051:0.435871:0.814051:0.000000 R:@0.454369:0.826856:0.467674:0.826856:0.467674:0.813994:0.454369:0.813994:0.000000 3:@0.467527:0.821592:0.472480:0.821592:0.472480:0.811974:0.467527:0.811974:0.000000 – = (– , – , – ) , – , que se opera como la suma de con el :@0.108232:0.845294:0.599929:0.845294:0.599929:0.828796:0.108232:0.828796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.118732:0.845410:0.126515:0.845410:0.126515:0.828941:0.118732:0.828941:0.000000 :@0.120735:0.845786:0.127151:0.845786:0.127151:0.829968:0.120735:0.829968:0.000000 x y z:@0.162888:0.845410:0.219682:0.845410:0.219682:0.828941:0.162888:0.828941:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.229859:0.844776:0.244511:0.844776:0.244511:0.831402:0.229859:0.831402:0.000000 R:@0.248452:0.844207:0.261757:0.844207:0.261757:0.831345:0.248452:0.831345:0.000000 3:@0.261610:0.838942:0.266563:0.838942:0.266563:0.829324:0.261610:0.829324:0.000000 u v:@0.273557:0.845410:0.309679:0.845410:0.309679:0.828941:0.273557:0.828941:0.000000:0.000000:0.000000 :@0.276504:0.845786:0.282920:0.845786:0.282920:0.829968:0.276504:0.829968:0.000000 :@0.303899:0.845786:0.310315:0.845786:0.310315:0.829968:0.303899:0.829968:0.000000 u:@0.539319:0.845410:0.548528:0.845410:0.548528:0.828941:0.539319:0.828941:0.000000 :@0.542249:0.845786:0.548664:0.845786:0.548664:0.829968:0.542249:0.829968:0.000000 opuesto aditivo de . :@0.108241:0.862645:0.261073:0.862645:0.261073:0.846147:0.108241:0.846147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.245755:0.862761:0.253538:0.862761:0.253538:0.846292:0.245755:0.846292:0.000000 :@0.247760:0.863137:0.254176:0.863137:0.254176:0.847318:0.247760:0.847318:0.000000 Ejercicio resuelto:@0.108241:0.897722:0.226220:0.897722:0.226220:0.880935:0.108241:0.880935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.108241:0.914914:0.120513:0.914914:0.120513:0.898199:0.108241:0.898199:0.000000:0.000000 Sean = (5, –2, 3), = (15, 3, –8). Entonces – = (–15, –3, 8), y :@0.120513:0.914698:0.583265:0.914698:0.583265:0.898200:0.120513:0.898200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.169775:0.914813:0.181045:0.914813:0.181045:0.898345:0.169775:0.898345:0.000000 :@0.172857:0.912674:0.179272:0.912674:0.179272:0.896855:0.172857:0.896855:0.000000 B:@0.271091:0.914813:0.280280:0.914813:0.280280:0.898345:0.271091:0.898345:0.000000 :@0.273537:0.912674:0.279953:0.912674:0.279953:0.896855:0.273537:0.896855:0.000000 B:@0.455767:0.914813:0.464957:0.914813:0.464957:0.898345:0.455767:0.898345:0.000000 :@0.458214:0.912674:0.464629:0.912674:0.464629:0.896855:0.458214:0.896855:0.000000 :@0.108241:0.932049:0.112383:0.932049:0.112383:0.915551:0.108241:0.915551:0.000000 A B A:@0.131976:0.932164:0.199482:0.932164:0.199482:0.915695:0.131976:0.915695:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.135059:0.930024:0.141474:0.930024:0.141474:0.914206:0.135059:0.914206:0.000000 – = +(– ) = (5, –2, 3) + (15, –3, 8) = (5 – 15, –2 – 3, 3 + 8):@0.141474:0.932049:0.585403:0.932049:0.585403:0.915551:0.141474:0.915551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.162704:0.930024:0.169120:0.930024:0.169120:0.914206:0.162704:0.914206:0.000000 :@0.191294:0.930024:0.197709:0.930024:0.197709:0.914206:0.191294:0.914206:0.000000 B:@0.229112:0.932164:0.238301:0.932164:0.238301:0.915695:0.229112:0.915695:0.000000 :@0.231558:0.930024:0.237974:0.930024:0.237974:0.914206:0.231558:0.914206:0.000000 :@0.108241:0.949399:0.112383:0.949399:0.112383:0.932902:0.108241:0.932902:0.000000 :@0.131995:0.949399:0.136137:0.949399:0.136137:0.932902:0.131995:0.932902:0.000000 = (–10, –5, 11).:@0.248955:0.949399:0.355839:0.949399:0.355839:0.932902:0.248955:0.932902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.360584:0.649486:0.369080:0.649486:0.369080:0.632988:0.360584:0.632988:0.000000 2:@0.360584:0.665824:0.369080:0.665824:0.369080:0.649327:0.360584:0.649327:0.000000 1:@0.317978:0.684146:0.326474:0.684146:0.326474:0.667648:0.317978:0.667648:0.000000 2:@0.317978:0.700485:0.326474:0.700485:0.326474:0.683987:0.317978:0.683987:0.000000 1 2:@0.509582:0.649486:0.544902:0.649486:0.544902:0.632988:0.509582:0.632988:0.000000:0.000000:0.000000 2 3:@0.509582:0.665824:0.544902:0.665824:0.544902:0.649327:0.509582:0.649327:0.000000:0.000000:0.000000 1 2:@0.421744:0.684146:0.457064:0.684146:0.457064:0.667648:0.421744:0.667648:0.000000:0.000000:0.000000 2 3:@0.421744:0.700485:0.457064:0.700485:0.457064:0.683987:0.421744:0.683987:0.000000:0.000000:0.000000 1:@0.199204:0.718984:0.207700:0.718984:0.207700:0.702487:0.199204:0.702487:0.000000 2:@0.199204:0.735323:0.207700:0.735323:0.207700:0.718825:0.199204:0.718825:0.000000 2:@0.271239:0.718984:0.279735:0.718984:0.279735:0.702487:0.271239:0.702487:0.000000 3:@0.271239:0.735323:0.279735:0.735323:0.279735:0.718825:0.271239:0.718825:0.000000 2:@0.398230:0.649486:0.406726:0.649486:0.406726:0.632988:0.398230:0.632988:0.000000 3:@0.398230:0.665824:0.406726:0.665824:0.406726:0.649327:0.398230:0.649327:0.000000 2:@0.355624:0.684146:0.364120:0.684146:0.364120:0.667648:0.355624:0.667648:0.000000 3:@0.355624:0.700485:0.364120:0.700485:0.364120:0.683987:0.355624:0.683987:0.000000 1:@0.234404:0.718984:0.242900:0.718984:0.242900:0.702487:0.234404:0.702487:0.000000 2:@0.234404:0.735323:0.242900:0.735323:0.242900:0.718825:0.234404:0.718825:0.000000 2:@0.305714:0.718984:0.314210:0.718984:0.314210:0.702487:0.305714:0.702487:0.000000 3:@0.305714:0.735323:0.314210:0.735323:0.314210:0.718825:0.305714:0.718825:0.000000 Competencia :@0.684804:0.096006:0.782426:0.096006:0.782426:0.080533:0.684804:0.080533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.684804:0.108574:0.768866:0.108574:0.768866:0.093101:0.684804:0.093101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Grupo conmutativo :@0.685042:0.133471:0.829014:0.133471:0.829014:0.117998:0.685042:0.117998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , +):@0.638498:0.149313:0.685390:0.149313:0.685390:0.133840:0.638498:0.133840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.644590:0.147888:0.656685:0.147888:0.656685:0.136195:0.644590:0.136195:0.000000 3:@0.656685:0.143336:0.661679:0.143336:0.661679:0.134316:0.656685:0.134316:0.000000 El conjunto en el que se :@0.638495:0.164732:0.816964:0.164732:0.816964:0.149669:0.638495:0.149669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.716779:0.163730:0.728874:0.163730:0.728874:0.152037:0.716779:0.152037:0.000000 3:@0.728874:0.158932:0.733397:0.158932:0.733397:0.150150:0.728874:0.150150:0.000000 ha definido la igualdad de :@0.638498:0.180574:0.810049:0.180574:0.810049:0.165511:0.638498:0.165511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 elementos de junto con la :@0.638498:0.196416:0.831758:0.196416:0.831758:0.181353:0.638498:0.181353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.729742:0.195413:0.741837:0.195413:0.741837:0.183721:0.729742:0.183721:0.000000 3:@0.741837:0.190616:0.746360:0.190616:0.746360:0.181834:0.741837:0.181834:0.000000 operación adición “+” tiene :@0.638497:0.212258:0.819867:0.212258:0.819867:0.197195:0.638497:0.197195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estructura algebraica de grupo :@0.638497:0.228100:0.839656:0.228100:0.839656:0.213037:0.638497:0.213037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 abeliano o conmutativo; esto :@0.638497:0.243942:0.831299:0.243942:0.831299:0.228879:0.638497:0.228879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es, la operación adición “+” es :@0.638497:0.259784:0.834588:0.259784:0.834588:0.244721:0.638497:0.244721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cerrada en y satisface las pro-:@0.638497:0.275626:0.846681:0.275626:0.846681:0.260563:0.638497:0.260563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.710153:0.274623:0.722249:0.274623:0.722249:0.262931:0.710153:0.262931:0.000000 3:@0.722247:0.269826:0.726769:0.269826:0.726769:0.261044:0.722247:0.261044:0.000000 piedades i) a iv) del teorema de :@0.638503:0.291468:0.845833:0.291468:0.845833:0.276405:0.638503:0.276405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la página 206.:@0.638503:0.307310:0.725539:0.307310:0.725539:0.292247:0.638503:0.292247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Teorema:@0.638503:0.339417:0.699627:0.339417:0.699627:0.323944:0.638503:0.323944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.699629:0.338994:0.702144:0.338994:0.702144:0.323931:0.699629:0.323931:0.000000 Sean = ( , , ), = ( , , ):@0.638503:0.354836:0.820466:0.354836:0.820466:0.339774:0.638503:0.339773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.673015:0.354942:0.681423:0.354942:0.681423:0.339906:0.673015:0.339906:0.000000 :@0.675706:0.355285:0.681563:0.355285:0.681563:0.340843:0.675706:0.340843:0.000000 a b c v:@0.704430:0.354942:0.759080:0.354942:0.759080:0.339906:0.704430:0.339906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.753803:0.355285:0.759660:0.355285:0.759660:0.340843:0.753803:0.340843:0.000000 x y z:@0.782526:0.354942:0.815031:0.354942:0.815031:0.339906:0.782526:0.339906:0.000000:0.000000:0.000000:0.000000:0.000000 dos elementos de . Entonces, :@0.638503:0.370678:0.847207:0.370678:0.847207:0.355615:0.638503:0.355615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.756883:0.369686:0.769030:0.369686:0.769030:0.357942:0.756883:0.357942:0.000000 3:@0.768894:0.364879:0.773416:0.364879:0.773416:0.356097:0.768894:0.356097:0.000000 –( + ) = (– ) + (– ).:@0.666364:0.393649:0.818796:0.393648:0.818796:0.378585:0.666364:0.378586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u v:@0.681386:0.393753:0.714472:0.393753:0.714472:0.378717:0.681386:0.378717:0.000000:0.000000:0.000000 :@0.684077:0.394096:0.689935:0.394096:0.689935:0.379654:0.684077:0.379654:0.000000 :@0.709195:0.394096:0.715052:0.394096:0.715052:0.379654:0.709195:0.379654:0.000000 u:@0.752941:0.393753:0.761348:0.393753:0.761348:0.378717:0.752941:0.378717:0.000000 :@0.755632:0.394096:0.761489:0.394096:0.761489:0.379654:0.755632:0.379654:0.000000 v:@0.803158:0.393753:0.810264:0.393753:0.810264:0.378717:0.803158:0.378717:0.000000 :@0.804987:0.394096:0.810844:0.394096:0.810844:0.379654:0.804987:0.379654:0.000000 Teorema :@0.638498:0.425754:0.705815:0.425754:0.705815:0.410282:0.638498:0.410282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Ley cancelativa.:@0.699624:0.425332:0.805795:0.425332:0.805795:0.410269:0.699624:0.410269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para todo , , :@0.638498:0.441174:0.751798:0.441174:0.751798:0.426111:0.638498:0.426111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B C:@0.705838:0.441279:0.747436:0.441279:0.747436:0.426243:0.705838:0.426243:0.000000:0.000000:0.000000:0.000000:0.000000   :@0.708652:0.439325:0.748017:0.439325:0.748017:0.424883:0.708652:0.424883:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.751796:0.440825:0.765751:0.440825:0.765751:0.428088:0.751796:0.428088:0.000000 :@0.765751:0.440976:0.770149:0.440976:0.770149:0.427602:0.765751:0.427602:0.000000 R:@0.770149:0.440171:0.782244:0.440171:0.782244:0.428478:0.770149:0.428478:0.000000 3:@0.782244:0.435374:0.786766:0.435374:0.786766:0.426593:0.782244:0.426593:0.000000 , :@0.786765:0.441174:0.793062:0.441174:0.793062:0.426111:0.786765:0.426111:0.000000:0.000000 A B A C:@0.666385:0.464249:0.754507:0.464249:0.754507:0.449213:0.666385:0.449213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.669199:0.462295:0.701194:0.462295:0.701194:0.447853:0.669199:0.447853:0.000000:0.000000:0.000000:0.000000 + = + :@0.679454:0.464143:0.758869:0.464143:0.758869:0.449081:0.679454:0.449081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.721439:0.462295:0.755087:0.462295:0.755087:0.447853:0.721439:0.447853:0.000000:0.000000:0.000000:0.000000 ⇔:@0.758869:0.463681:0.777197:0.463681:0.777197:0.447510:0.758869:0.447510:0.000000 = .:@0.777197:0.464143:0.818760:0.464143:0.818760:0.449081:0.777197:0.449081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B C:@0.780979:0.464249:0.815664:0.464249:0.815664:0.449213:0.780979:0.449213:0.000000:0.000000:0.000000 :@0.783212:0.462295:0.789070:0.462295:0.789070:0.447853:0.783212:0.447853:0.000000 :@0.810388:0.462295:0.816245:0.462295:0.816245:0.447853:0.810388:0.447853:0.000000 Teorema :@0.638503:0.496250:0.705820:0.496250:0.705820:0.480777:0.638503:0.480777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.699629:0.495827:0.702144:0.495827:0.702144:0.480764:0.699629:0.480764:0.000000 i.:@0.638503:0.511867:0.645451:0.511867:0.645451:0.496606:0.638503:0.496606:0.000000:0.000000 El elemento 0 de es único.:@0.645452:0.511669:0.843525:0.511669:0.843525:0.496606:0.645452:0.496606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.736530:0.509821:0.742387:0.509821:0.742387:0.495379:0.736530:0.495379:0.000000 R:@0.767048:0.510667:0.779143:0.510667:0.779143:0.498974:0.767048:0.498974:0.000000 3:@0.779141:0.505870:0.783664:0.505870:0.783664:0.497089:0.779141:0.497089:0.000000 ii.:@0.638512:0.527709:0.649347:0.527709:0.649347:0.512448:0.638512:0.512448:0.000000:0.000000:0.000000 Dado :@0.649347:0.527511:0.707382:0.527511:0.707382:0.512448:0.649347:0.512448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.695053:0.527617:0.703460:0.527617:0.703460:0.512581:0.695053:0.512581:0.000000 :@0.697744:0.527960:0.703601:0.527960:0.703601:0.513518:0.697744:0.513518:0.000000 :@0.707383:0.527162:0.721337:0.527162:0.721337:0.514426:0.707383:0.514426:0.000000 :@0.721337:0.527313:0.725735:0.527313:0.725735:0.513940:0.721337:0.513940:0.000000 R:@0.725735:0.526509:0.737830:0.526509:0.737830:0.514816:0.725735:0.514816:0.000000 3:@0.737830:0.521712:0.742352:0.521712:0.742352:0.512931:0.737830:0.512931:0.000000 , el opuesto :@0.742351:0.527511:0.820414:0.527511:0.820414:0.512448:0.742351:0.512448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aditivo – :@0.655123:0.543353:0.725201:0.543353:0.725201:0.528290:0.655123:0.528290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.712872:0.543459:0.721280:0.543459:0.721280:0.528423:0.712872:0.528423:0.000000 :@0.715563:0.543802:0.721421:0.543802:0.721421:0.529360:0.715563:0.529360:0.000000 :@0.725202:0.543004:0.739157:0.543004:0.739157:0.530268:0.725202:0.530268:0.000000 :@0.739157:0.543155:0.743554:0.543155:0.743554:0.529782:0.739157:0.529782:0.000000 R:@0.743554:0.542351:0.755650:0.542351:0.755650:0.530658:0.743554:0.530658:0.000000 3:@0.755650:0.537554:0.760172:0.537554:0.760172:0.528773:0.755650:0.528773:0.000000 es único.:@0.760171:0.543353:0.820028:0.543353:0.820028:0.528290:0.760171:0.528290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000 maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000 ®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000