147:@0.918240:0.967835:0.943652:0.967835:0.943652:0.951847:0.918240:0.951847:0.000000:0.000000:0.000000 Demostración:@0.108233:0.096657:0.217525:0.096657:0.217525:0.079711:0.108233:0.079711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean :@0.108233:0.121303:0.145654:0.121303:0.145654:0.104805:0.108233:0.104805:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.173190:0.124972:0.179606:0.124972:0.179606:0.103481:0.173190:0.103481:0.000000 ):@0.206173:0.124972:0.212588:0.124972:0.212588:0.103481:0.206173:0.103481:0.000000 (:@0.248941:0.124972:0.255357:0.124972:0.255357:0.103481:0.248941:0.103481:0.000000 ):@0.281500:0.124972:0.287915:0.124972:0.287915:0.103481:0.281500:0.103481:0.000000 (:@0.329929:0.124972:0.336345:0.124972:0.336345:0.103481:0.329929:0.103481:0.000000 ):@0.364491:0.124972:0.370906:0.124972:0.370906:0.103481:0.364491:0.103481:0.000000 =:@0.159892:0.121303:0.170700:0.121303:0.170700:0.104805:0.159892:0.104805:0.000000 ,:@0.190197:0.121303:0.192952:0.121303:0.192952:0.104805:0.190197:0.104805:0.000000 ,= ,:@0.214760:0.121303:0.267508:0.121303:0.267508:0.104805:0.214760:0.104805:0.000000:0.000000:0.000000:0.000000 ,:@0.290087:0.121303:0.292842:0.121303:0.292842:0.104805:0.290087:0.104805:0.000000 =:@0.316633:0.121303:0.327441:0.121303:0.327441:0.104805:0.316633:0.104805:0.000000 ,:@0.348093:0.121303:0.350848:0.121303:0.350848:0.104805:0.348093:0.104805:0.000000 U:@0.145018:0.121418:0.156962:0.121418:0.156962:0.104949:0.145018:0.104949:0.000000 a bV:@0.180312:0.121418:0.231533:0.121418:0.231533:0.104949:0.180312:0.104949:0.000000:0.000000:0.000000:0.000000 cd W:@0.256058:0.121418:0.312410:0.121418:0.312410:0.104949:0.256058:0.104949:0.000000:0.000000:0.000000:0.000000 p q:@0.337782:0.121418:0.364124:0.121418:0.364124:0.104949:0.337782:0.104949:0.000000:0.000000:0.000000 tres elementos arbitrarios de . :@0.371162:0.121303:0.599869:0.121303:0.599869:0.104805:0.371162:0.104805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.574362:0.120334:0.588132:0.120334:0.588132:0.106887:0.574362:0.106887:0.000000 2:@0.588137:0.114949:0.593041:0.114949:0.593041:0.105331:0.588137:0.105331:0.000000 i) Conmutativa.:@0.108233:0.145998:0.233184:0.145998:0.233184:0.129283:0.108233:0.129283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.118771:0.145781:0.135821:0.145781:0.135821:0.129283:0.118771:0.129283:0.000000:0.000000 De la definición de suma de elementos en :@0.233188:0.145781:0.552217:0.145781:0.552217:0.129283:0.233188:0.129283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.553820:0.144812:0.567730:0.144812:0.567730:0.131365:0.553820:0.131365:0.000000 2:@0.567753:0.139429:0.572706:0.139429:0.572706:0.129811:0.567753:0.129811:0.000000 , se :@0.572705:0.145781:0.599908:0.145781:0.599908:0.129283:0.572705:0.129283:0.000000:0.000000:0.000000:0.000000:0.000000 tiene :@0.131685:0.163508:0.171390:0.163508:0.171390:0.147010:0.131685:0.147010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.227460:0.167431:0.233875:0.167431:0.233875:0.145940:0.227460:0.145940:0.000000 ) (:@0.260442:0.167431:0.287433:0.167431:0.287433:0.145940:0.260442:0.145940:0.000000:0.000000:0.000000 ) (:@0.313576:0.167431:0.342556:0.167431:0.342556:0.145940:0.313576:0.145940:0.000000:0.000000:0.000000 ):@0.415514:0.167431:0.421929:0.167431:0.421929:0.145940:0.415514:0.145940:0.000000 +:@0.187202:0.164397:0.197779:0.164397:0.197779:0.148116:0.187202:0.148116:0.000000 +:@0.268502:0.164397:0.279078:0.164397:0.279078:0.148116:0.268502:0.148116:0.000000 +:@0.353731:0.164397:0.364308:0.164397:0.364308:0.148116:0.353731:0.148116:0.000000 +:@0.392685:0.164397:0.403262:0.164397:0.403262:0.148116:0.392685:0.148116:0.000000 =:@0.214163:0.163760:0.224971:0.163760:0.224971:0.147263:0.214163:0.147263:0.000000 ,:@0.244468:0.163760:0.247223:0.163760:0.247223:0.147263:0.244468:0.147263:0.000000 ,:@0.296831:0.163760:0.299586:0.163760:0.299586:0.147263:0.296831:0.147263:0.000000 =:@0.322858:0.163760:0.333666:0.163760:0.333666:0.147263:0.322858:0.147263:0.000000 ,:@0.375352:0.163760:0.378107:0.163760:0.378107:0.147263:0.375352:0.147263:0.000000 .:@0.423361:0.163760:0.426116:0.163760:0.426116:0.147263:0.423361:0.147263:0.000000 UV:@0.173539:0.163876:0.210047:0.163876:0.210047:0.147407:0.173539:0.147407:0.000000:0.000000 ab:@0.234571:0.163876:0.260175:0.163876:0.260175:0.147407:0.234571:0.147407:0.000000:0.000000 cd:@0.288129:0.163876:0.312846:0.163876:0.312846:0.147407:0.288129:0.147407:0.000000:0.000000 ac bd:@0.343247:0.163876:0.414773:0.163876:0.414773:0.147407:0.343247:0.147407:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108233:0.188490:0.112375:0.188490:0.112375:0.171992:0.108233:0.171992:0.000000 Además :@0.131687:0.188490:0.194412:0.188490:0.194412:0.171992:0.131687:0.171992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.250481:0.192286:0.256896:0.192286:0.256896:0.170796:0.250481:0.170796:0.000000 ) (:@0.283039:0.192286:0.310030:0.192286:0.310030:0.170796:0.283039:0.170796:0.000000:0.000000:0.000000 ) (:@0.336597:0.192286:0.365578:0.192286:0.365578:0.170796:0.336597:0.170796:0.000000:0.000000:0.000000 ):@0.438535:0.192286:0.444950:0.192286:0.444950:0.170796:0.438535:0.170796:0.000000 +:@0.210223:0.189252:0.220800:0.189252:0.220800:0.172971:0.210223:0.172971:0.000000 +:@0.291099:0.189252:0.301675:0.189252:0.301675:0.172971:0.291099:0.172971:0.000000 +:@0.375549:0.189252:0.386126:0.189252:0.386126:0.172971:0.375549:0.172971:0.000000 +:@0.416488:0.189252:0.427065:0.189252:0.427065:0.172971:0.416488:0.172971:0.000000 =,:@0.237185:0.188616:0.269049:0.188616:0.269049:0.172118:0.237185:0.172118:0.000000:0.000000 ,:@0.320642:0.188616:0.323397:0.188616:0.323397:0.172118:0.320642:0.172118:0.000000 =:@0.345879:0.188616:0.356687:0.188616:0.356687:0.172118:0.345879:0.172118:0.000000 ,:@0.398375:0.188616:0.401129:0.188616:0.401129:0.172118:0.398375:0.172118:0.000000 , y por la propiedad :@0.447116:0.188616:0.596680:0.188486:0.596680:0.171988:0.447116:0.172118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 VU:@0.196560:0.188732:0.234262:0.188732:0.234262:0.172263:0.196560:0.172263:0.000000:0.000000 cd:@0.257592:0.188732:0.282310:0.188732:0.282310:0.172263:0.257592:0.172263:0.000000:0.000000 ab:@0.310726:0.188732:0.336329:0.188732:0.336329:0.172263:0.310726:0.172263:0.000000:0.000000 ca db:@0.366268:0.188732:0.438262:0.188732:0.438262:0.172263:0.366268:0.172263:0.000000:0.000000:0.000000:0.000000:0.000000 con mutativa de la operación “+” en , obtenemos :@0.131675:0.205837:0.494954:0.205841:0.494954:0.189343:0.131675:0.189339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.388747:0.204872:0.402656:0.204872:0.402656:0.191425:0.388747:0.191425:0.000000 (:@0.187755:0.227491:0.194170:0.227491:0.194170:0.206000:0.187755:0.206000:0.000000 ):@0.267128:0.227491:0.273543:0.227491:0.273543:0.206000:0.267128:0.206000:0.000000 +:@0.147497:0.224457:0.158074:0.224457:0.158074:0.208176:0.147497:0.208176:0.000000 +:@0.205351:0.224457:0.215928:0.224457:0.215928:0.208176:0.205351:0.208176:0.000000 +:@0.244286:0.224457:0.254863:0.224457:0.254863:0.208176:0.244286:0.208176:0.000000 =:@0.174449:0.223820:0.185257:0.223820:0.185257:0.207323:0.174449:0.207323:0.000000 ,:@0.226967:0.223820:0.229721:0.223820:0.229721:0.207323:0.226967:0.207323:0.000000 VU:@0.133819:0.223936:0.171521:0.223936:0.171521:0.207467:0.133819:0.207467:0.000000:0.000000 ac bd:@0.194851:0.223936:0.266387:0.223936:0.266387:0.207467:0.194851:0.207467:0.000000:0.000000:0.000000:0.000000:0.000000 . Por la definición de igualdad de elementos :@0.273961:0.223820:0.586785:0.223820:0.586785:0.207323:0.273961:0.207323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en , se tiene :@0.131687:0.241547:0.237550:0.241548:0.237550:0.225051:0.131687:0.225049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.153379:0.240578:0.167289:0.240578:0.167289:0.227131:0.153379:0.227131:0.000000 2:@0.167289:0.235197:0.172242:0.235197:0.172242:0.225578:0.167289:0.225578:0.000000 (:@0.347121:0.245470:0.353536:0.245470:0.353536:0.223979:0.347121:0.223979:0.000000 ):@0.426493:0.245470:0.432909:0.245470:0.432909:0.223979:0.426493:0.223979:0.000000 +:@0.253359:0.242436:0.263936:0.242436:0.263936:0.226155:0.253359:0.226155:0.000000 +:@0.306859:0.242436:0.317435:0.242436:0.317435:0.226155:0.306859:0.226155:0.000000 +:@0.364711:0.242436:0.375287:0.242436:0.375287:0.226155:0.364711:0.226155:0.000000 +:@0.403665:0.242436:0.414242:0.242436:0.414242:0.226155:0.403665:0.226155:0.000000 =:@0.280320:0.241800:0.291128:0.241800:0.291128:0.225302:0.280320:0.225302:0.000000 =:@0.333820:0.241800:0.344628:0.241800:0.344628:0.225302:0.333820:0.225302:0.000000 ,:@0.386331:0.241800:0.389086:0.241800:0.389086:0.225302:0.386331:0.225302:0.000000 . :@0.434340:0.241800:0.444396:0.241548:0.444396:0.225051:0.434340:0.225302:0.000000:0.000000:0.000000 UV VU:@0.239696:0.241915:0.330898:0.241915:0.330898:0.225447:0.239696:0.225447:0.000000:0.000000:0.000000:0.000000:0.000000 ac bd:@0.354228:0.241915:0.425753:0.241915:0.425753:0.225447:0.354228:0.225447:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108236:0.266028:0.112378:0.266028:0.112378:0.249530:0.108236:0.249530:0.000000 Conclusión:@0.131681:0.266491:0.218163:0.266491:0.218163:0.249545:0.131681:0.249545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : :@0.218163:0.266028:0.225060:0.266028:0.225060:0.249530:0.218163:0.249530:0.000000:0.000000 UV VU:@0.227210:0.266144:0.321552:0.266144:0.321552:0.249675:0.227210:0.249675:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.241717:0.266664:0.197272:0.266664:0.197272:0.250383:0.241717:0.250383:0.000000 +:@0.296739:0.266664:0.252294:0.266664:0.252294:0.250383:0.296739:0.250383:0.000000 =:@0.269401:0.266028:0.280209:0.266028:0.280209:0.249530:0.269401:0.249530:0.000000 .:@0.321957:0.266028:0.324712:0.266028:0.324712:0.249530:0.321957:0.249530:0.000000 ii) Asociativa.:@0.108233:0.290723:0.212053:0.290723:0.212053:0.274009:0.108233:0.274009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.123029:0.290506:0.127171:0.290506:0.127171:0.274009:0.123029:0.274009:0.000000 Por la definición de la adición “+” en :@0.212054:0.290506:0.505366:0.290506:0.505366:0.274009:0.212054:0.274009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.508816:0.289538:0.522726:0.289538:0.522726:0.276091:0.508816:0.276091:0.000000 2:@0.522748:0.284153:0.527701:0.284153:0.527701:0.274535:0.522748:0.274535:0.000000 , se tiene :@0.527700:0.290506:0.599906:0.290506:0.599906:0.274009:0.527700:0.274009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.195816:0.311421:0.202232:0.311421:0.202232:0.289442:0.195816:0.289442:0.000000 ) (:@0.230937:0.311421:0.258717:0.311421:0.258717:0.289442:0.230937:0.289442:0.000000:0.000000:0.000000 ) (:@0.289426:0.311421:0.318767:0.311421:0.318767:0.289442:0.289426:0.289442:0.000000:0.000000:0.000000 ):@0.397369:0.311421:0.403785:0.311421:0.403785:0.289442:0.397369:0.289442:0.000000 +:@0.148335:0.309122:0.158912:0.309122:0.158912:0.292841:0.148335:0.292841:0.000000 =:@0.182145:0.309122:0.192722:0.309122:0.192722:0.292841:0.182145:0.292841:0.000000 +:@0.239421:0.309122:0.249998:0.309122:0.249998:0.292841:0.239421:0.292841:0.000000 =:@0.298681:0.309122:0.309258:0.309122:0.309258:0.292841:0.298681:0.292841:0.000000 +:@0.329993:0.309122:0.340570:0.309122:0.340570:0.292841:0.329993:0.292841:0.000000 +:@0.373706:0.309122:0.384282:0.309122:0.384282:0.292841:0.373706:0.292841:0.000000 VW:@0.133832:0.308601:0.177507:0.308601:0.177507:0.292133:0.133832:0.292133:0.000000:0.000000 cd:@0.203361:0.308601:0.229812:0.308601:0.229812:0.292133:0.203361:0.292133:0.000000:0.000000 pq:@0.260579:0.308601:0.288648:0.308601:0.288648:0.292133:0.260579:0.292133:0.000000:0.000000 cp dq:@0.319896:0.308601:0.396599:0.308601:0.396599:0.292133:0.319896:0.292133:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.212046:0.308486:0.214801:0.308486:0.214801:0.291988:0.212046:0.291988:0.000000 ,:@0.270882:0.308486:0.273637:0.308486:0.273637:0.291988:0.270882:0.291988:0.000000 ,:@0.354763:0.308486:0.357518:0.308486:0.357518:0.291988:0.354763:0.291988:0.000000 .:@0.406432:0.308486:0.409187:0.308486:0.409187:0.291988:0.406432:0.291988:0.000000 :@0.108238:0.335726:0.112380:0.335726:0.112380:0.319229:0.108238:0.319229:0.000000 Luego, y debido a la propiedad asociativa de la adición en , :@0.131684:0.335726:0.568389:0.335726:0.568389:0.319229:0.131684:0.319229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.543440:0.334758:0.557350:0.334758:0.557350:0.321311:0.543440:0.321311:0.000000 resulta :@0.131684:0.355839:0.183045:0.355839:0.183045:0.339341:0.131684:0.339341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.210843:0.358782:0.216883:0.358782:0.216883:0.336803:0.210843:0.336803:0.000000 ) (:@0.260229:0.358782:0.287851:0.358782:0.287851:0.336803:0.260229:0.336803:0.000000:0.000000:0.000000 ) (:@0.315673:0.358782:0.341826:0.358782:0.341826:0.336803:0.315673:0.336803:0.000000:0.000000:0.000000 ):@0.417456:0.358782:0.423495:0.358782:0.423495:0.336803:0.417456:0.336803:0.000000 +:@0.198719:0.356483:0.208676:0.356483:0.208676:0.340202:0.198719:0.340202:0.000000 +:@0.230803:0.356483:0.240760:0.356483:0.240760:0.340202:0.230803:0.340202:0.000000 =:@0.268944:0.356483:0.278902:0.356483:0.278902:0.340202:0.268944:0.340202:0.000000 + +:@0.323645:0.356483:0.362348:0.356483:0.362348:0.340202:0.323645:0.340202:0.000000:0.000000:0.000000 +:@0.395176:0.356483:0.405133:0.356483:0.405133:0.340202:0.395176:0.340202:0.000000 U:@0.185063:0.355963:0.196307:0.355963:0.196307:0.339494:0.185063:0.339494:0.000000 V W:@0.217146:0.355963:0.258262:0.355963:0.258262:0.339494:0.217146:0.339494:0.000000:0.000000:0.000000 a b:@0.288895:0.355963:0.315030:0.355963:0.315030:0.339494:0.288895:0.339494:0.000000:0.000000:0.000000 c pd q:@0.342869:0.355963:0.416722:0.355963:0.416722:0.339494:0.342869:0.339494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.298235:0.355847:0.300829:0.355847:0.300829:0.339349:0.298235:0.339349:0.000000 ,:@0.375715:0.355847:0.378308:0.355847:0.378308:0.339349:0.375715:0.339349:0.000000 , :@0.424971:0.355847:0.431868:0.355847:0.431868:0.339349:0.424971:0.339349:0.000000:0.000000 a:@0.434851:0.354705:0.443829:0.354705:0.443829:0.338237:0.434851:0.338237:0.000000 c p:@0.466581:0.354705:0.500392:0.354705:0.500392:0.338237:0.466581:0.338237:0.000000:0.000000:0.000000 a cp:@0.523529:0.354705:0.582388:0.354705:0.582388:0.338237:0.523529:0.338237:0.000000:0.000000:0.000000:0.000000 (:@0.459037:0.357525:0.465452:0.357525:0.465452:0.335546:0.459037:0.335546:0.000000 ):@0.501073:0.357525:0.507489:0.357525:0.507489:0.335546:0.501073:0.335546:0.000000 +:@0.446159:0.355226:0.456736:0.355226:0.456736:0.338945:0.446159:0.338945:0.000000 +:@0.476675:0.355226:0.487252:0.355226:0.487252:0.338945:0.476675:0.338945:0.000000 ++:@0.534837:0.355226:0.569226:0.355226:0.569226:0.338945:0.534837:0.338945:0.000000:0.000000 =:@0.509870:0.354590:0.520678:0.354590:0.520678:0.338092:0.509870:0.338092:0.000000 , :@0.583425:0.354590:0.593482:0.355847:0.593482:0.339349:0.583425:0.338092:0.000000:0.000000:0.000000 b:@0.134251:0.376079:0.143518:0.376079:0.143518:0.359611:0.134251:0.359611:0.000000 d q:@0.166405:0.376079:0.201371:0.376079:0.201371:0.359611:0.166405:0.359611:0.000000:0.000000:0.000000 b dq:@0.224181:0.376079:0.284619:0.376079:0.284619:0.359611:0.224181:0.359611:0.000000:0.000000:0.000000:0.000000 (:@0.158857:0.378899:0.165272:0.378899:0.165272:0.356920:0.158857:0.356920:0.000000 ):@0.202146:0.378899:0.208561:0.378899:0.208561:0.356920:0.202146:0.356920:0.000000 +:@0.145978:0.376600:0.156555:0.376600:0.156555:0.360319:0.145978:0.360319:0.000000 +:@0.178498:0.376600:0.189074:0.376600:0.189074:0.360319:0.178498:0.360319:0.000000 ++:@0.235908:0.376600:0.272300:0.376600:0.272300:0.360319:0.235908:0.360319:0.000000:0.000000 =:@0.210947:0.375964:0.221755:0.375964:0.221755:0.359466:0.210947:0.359466:0.000000 , con lo cual :@0.285754:0.375964:0.378392:0.375964:0.378392:0.359466:0.285754:0.359466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 U:@0.133832:0.396196:0.145777:0.396196:0.145777:0.379728:0.133832:0.379728:0.000000 V W:@0.167913:0.396196:0.211587:0.396196:0.211587:0.379728:0.167913:0.379728:0.000000:0.000000:0.000000 a cp bd q:@0.242816:0.396196:0.366884:0.396196:0.366884:0.379728:0.242816:0.379728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.161213:0.399016:0.167628:0.399016:0.167628:0.377037:0.161213:0.377037:0.000000 ) (:@0.213672:0.399016:0.241703:0.399016:0.241703:0.377037:0.213672:0.377037:0.000000:0.000000:0.000000 ):@0.367678:0.399016:0.374094:0.399016:0.374094:0.377037:0.367678:0.377037:0.000000 +:@0.148335:0.396717:0.158912:0.396717:0.158912:0.380436:0.148335:0.380436:0.000000 +:@0.182415:0.396717:0.192992:0.396717:0.192992:0.380436:0.182415:0.380436:0.000000 ++:@0.254140:0.396717:0.288528:0.396717:0.288528:0.380436:0.254140:0.380436:0.000000:0.000000 ++:@0.318216:0.396717:0.354608:0.396717:0.354608:0.380436:0.318216:0.380436:0.000000:0.000000 =:@0.222468:0.396081:0.233275:0.396081:0.233275:0.379583:0.222468:0.379583:0.000000 ,:@0.302727:0.396081:0.305482:0.396081:0.305482:0.379583:0.302727:0.379583:0.000000 .:@0.375068:0.396081:0.377823:0.396081:0.377823:0.379583:0.375068:0.379583:0.000000 :@0.108233:0.421188:0.112375:0.421188:0.112375:0.404690:0.108233:0.404690:0.000000 Por otro lado, :@0.131687:0.421188:0.232013:0.421188:0.232013:0.404690:0.131687:0.404690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 UV:@0.234166:0.421303:0.272292:0.421303:0.272292:0.404835:0.234166:0.404835:0.000000:0.000000 ab:@0.296720:0.421303:0.319646:0.421303:0.319646:0.404835:0.296720:0.404835:0.000000:0.000000 cd:@0.349237:0.421303:0.371296:0.421303:0.371296:0.404835:0.349237:0.404835:0.000000:0.000000 ac bd:@0.401581:0.421303:0.473687:0.421303:0.473687:0.404835:0.401581:0.404835:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) ( ) (:@0.289186:0.424123:0.400462:0.424123:0.400462:0.402144:0.289186:0.402144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.474826:0.424123:0.481241:0.424123:0.481241:0.402144:0.474826:0.402144:0.000000 +:@0.248667:0.421824:0.259243:0.421824:0.259243:0.405543:0.248667:0.405543:0.000000 +:@0.328810:0.421824:0.339387:0.421824:0.339387:0.405543:0.328810:0.405543:0.000000 +:@0.412892:0.421824:0.423469:0.421824:0.423469:0.405543:0.412892:0.405543:0.000000 +:@0.450787:0.421824:0.461364:0.421824:0.461364:0.405543:0.450787:0.405543:0.000000 =:@0.276360:0.421188:0.287168:0.421188:0.287168:0.404690:0.276360:0.404690:0.000000 ,:@0.306626:0.421188:0.309381:0.421188:0.309381:0.404690:0.306626:0.404690:0.000000 ,:@0.357929:0.421188:0.360684:0.421188:0.360684:0.404690:0.357929:0.404690:0.000000 =:@0.381221:0.421188:0.392029:0.421188:0.392029:0.404690:0.381221:0.404690:0.000000 ,:@0.435298:0.421188:0.438053:0.421188:0.438053:0.404690:0.435298:0.404690:0.000000 . Luego, :@0.482209:0.421188:0.542579:0.421188:0.542579:0.404690:0.482209:0.404690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 UV:@0.140533:0.440541:0.178659:0.440541:0.178659:0.424073:0.140533:0.424073:0.000000:0.000000 W:@0.201990:0.440541:0.218288:0.440541:0.218288:0.424073:0.201990:0.424073:0.000000 a cb d:@0.242832:0.440541:0.314903:0.440541:0.314903:0.424073:0.242832:0.424073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p q:@0.345670:0.440541:0.369347:0.440541:0.369347:0.424073:0.345670:0.424073:0.000000:0.000000:0.000000 a c:@0.405989:0.440541:0.438201:0.440541:0.438201:0.424073:0.405989:0.424073:0.000000:0.000000:0.000000 p bd:@0.462263:0.440541:0.517670:0.440541:0.517670:0.424073:0.462263:0.424073:0.000000:0.000000:0.000000:0.000000 q:@0.541000:0.440541:0.550170:0.440541:0.550170:0.424073:0.541000:0.424073:0.000000 (:@0.391767:0.445215:0.398183:0.445215:0.398183:0.419654:0.391767:0.419654:0.000000 ):@0.550975:0.445215:0.557391:0.445215:0.557391:0.419654:0.550975:0.419654:0.000000 (:@0.133832:0.443361:0.140248:0.443361:0.140248:0.421382:0.133832:0.421382:0.000000 ):@0.180628:0.443361:0.187043:0.443361:0.187043:0.421382:0.180628:0.421382:0.000000 (:@0.235283:0.443361:0.241699:0.443361:0.241699:0.421382:0.235283:0.421382:0.000000 ) (:@0.316062:0.443361:0.343843:0.443361:0.343843:0.421382:0.316062:0.421382:0.000000:0.000000:0.000000 ) (:@0.370140:0.443361:0.404875:0.443361:0.404875:0.421382:0.370140:0.421382:0.000000:0.000000:0.000000 ):@0.439341:0.443361:0.445756:0.443361:0.445756:0.421382:0.439341:0.421382:0.000000 (:@0.475945:0.443361:0.482360:0.443361:0.482360:0.421382:0.475945:0.421382:0.000000 ):@0.518829:0.443361:0.525245:0.443361:0.525245:0.421382:0.518829:0.421382:0.000000 +:@0.155036:0.441062:0.165613:0.441062:0.165613:0.424781:0.155036:0.424781:0.000000 +:@0.189116:0.441062:0.199693:0.441062:0.199693:0.424781:0.189116:0.424781:0.000000 +:@0.254136:0.441062:0.264713:0.441062:0.264713:0.424781:0.254136:0.424781:0.000000 +:@0.292031:0.441062:0.302608:0.441062:0.302608:0.424781:0.292031:0.424781:0.000000 +:@0.324551:0.441062:0.335128:0.441062:0.335128:0.424781:0.324551:0.424781:0.000000 +:@0.417313:0.441062:0.427890:0.441062:0.427890:0.424781:0.417313:0.424781:0.000000 +:@0.447829:0.441062:0.458406:0.441062:0.458406:0.424781:0.447829:0.424781:0.000000 +:@0.494798:0.441062:0.505375:0.441062:0.505375:0.424781:0.494798:0.424781:0.000000 +:@0.527298:0.441062:0.537875:0.441062:0.537875:0.424781:0.527298:0.424781:0.000000 =:@0.222464:0.440426:0.233272:0.440426:0.233272:0.423928:0.222464:0.423928:0.000000 ,:@0.276542:0.440426:0.279297:0.440426:0.279297:0.423928:0.276542:0.423928:0.000000 ,:@0.356011:0.440426:0.358766:0.440426:0.358766:0.423928:0.356011:0.423928:0.000000 =:@0.378937:0.440426:0.389745:0.440426:0.389745:0.423928:0.378937:0.423928:0.000000 ,:@0.472598:0.440426:0.475353:0.440426:0.475353:0.423928:0.472598:0.423928:0.000000 .:@0.558347:0.440426:0.561102:0.440426:0.561102:0.423928:0.558347:0.423928:0.000000 :@0.108233:0.464904:0.112375:0.464904:0.112375:0.448406:0.108233:0.448406:0.000000 Por la misma propiedad asociativa de la adición en , se obtiene :@0.131680:0.464904:0.599901:0.464904:0.599901:0.448406:0.131680:0.448406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.501072:0.463935:0.514981:0.463935:0.514981:0.450488:0.501072:0.450488:0.000000 UV:@0.144676:0.482999:0.182802:0.482999:0.182802:0.466530:0.144676:0.466530:0.000000:0.000000 W:@0.206132:0.482999:0.222431:0.482999:0.222431:0.466530:0.206132:0.466530:0.000000 a cp bd q:@0.246975:0.482999:0.371024:0.482999:0.371024:0.466530:0.246975:0.466530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.137975:0.485819:0.144391:0.485819:0.144391:0.463839:0.137975:0.463839:0.000000 ):@0.184771:0.485819:0.191186:0.485819:0.191186:0.463839:0.184771:0.463839:0.000000 (:@0.239426:0.485819:0.245841:0.485819:0.245841:0.463839:0.239426:0.463839:0.000000 ):@0.371817:0.485819:0.378232:0.485819:0.378232:0.463839:0.371817:0.463839:0.000000 +:@0.159177:0.483520:0.169754:0.483520:0.169754:0.467239:0.159177:0.467239:0.000000 +:@0.193257:0.483520:0.203834:0.483520:0.203834:0.467239:0.193257:0.467239:0.000000 ++:@0.258278:0.483520:0.292666:0.483520:0.292666:0.467239:0.258278:0.467239:0.000000:0.000000 ++:@0.322354:0.483520:0.358746:0.483520:0.358746:0.467239:0.322354:0.467239:0.000000:0.000000 =:@0.226605:0.482883:0.237413:0.482883:0.237413:0.466386:0.226605:0.466386:0.000000 ,:@0.306865:0.482883:0.309619:0.482883:0.309619:0.466386:0.306865:0.466386:0.000000 .:@0.379206:0.482883:0.381961:0.482883:0.381961:0.466386:0.379206:0.466386:0.000000 :@0.108233:0.507362:0.112375:0.507362:0.112375:0.490864:0.108233:0.490864:0.000000 De la definición de igualdad de elementos de , se concluye que :@0.131687:0.507362:0.599897:0.507362:0.599897:0.490864:0.131687:0.490864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.456241:0.506393:0.470150:0.506393:0.470150:0.492946:0.456241:0.492946:0.000000 2:@0.470185:0.501010:0.475139:0.501010:0.475139:0.491392:0.470185:0.491392:0.000000 :@0.595755:0.507362:0.599897:0.507362:0.599897:0.490864:0.595755:0.490864:0.000000 U:@0.133832:0.526714:0.145777:0.526714:0.145777:0.510245:0.133832:0.510245:0.000000 V W:@0.167913:0.526714:0.211587:0.526714:0.211587:0.510245:0.167913:0.510245:0.000000:0.000000:0.000000 a b:@0.242816:0.526714:0.265761:0.526714:0.265761:0.510245:0.242816:0.510245:0.000000:0.000000:0.000000 c pd q:@0.295333:0.526714:0.369369:0.526714:0.369369:0.510245:0.295333:0.510245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.399308:0.526714:0.408285:0.526714:0.408285:0.510245:0.399308:0.510245:0.000000 cp b:@0.431038:0.526714:0.486695:0.526714:0.486695:0.510245:0.431038:0.510245:0.000000:0.000000:0.000000:0.000000 d q:@0.509582:0.526714:0.544548:0.526714:0.544548:0.510245:0.509582:0.510245:0.000000:0.000000:0.000000 (:@0.391767:0.531389:0.398183:0.531389:0.398183:0.505828:0.391767:0.505828:0.000000 ):@0.552016:0.531389:0.558431:0.531389:0.558431:0.505828:0.552016:0.505828:0.000000 (:@0.161213:0.529534:0.167628:0.529534:0.167628:0.507555:0.161213:0.507555:0.000000 ) ( ) (:@0.213672:0.529534:0.294220:0.529534:0.294220:0.507555:0.213672:0.507555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.370163:0.529534:0.376579:0.529534:0.376579:0.507555:0.370163:0.507555:0.000000 (:@0.423490:0.529534:0.429905:0.529534:0.429905:0.507555:0.423490:0.507555:0.000000 ):@0.465526:0.529534:0.471942:0.529534:0.471942:0.507555:0.465526:0.507555:0.000000 (:@0.502015:0.529534:0.508430:0.529534:0.508430:0.507555:0.502015:0.507555:0.000000 ):@0.545304:0.529534:0.551719:0.529534:0.551719:0.507555:0.545304:0.507555:0.000000 +:@0.148335:0.527235:0.158912:0.527235:0.158912:0.510954:0.148335:0.510954:0.000000 +:@0.182415:0.527235:0.192992:0.527235:0.192992:0.510954:0.182415:0.510954:0.000000 +:@0.274927:0.527235:0.285504:0.527235:0.285504:0.510954:0.274927:0.510954:0.000000 +:@0.305443:0.527235:0.316020:0.527235:0.316020:0.510954:0.305443:0.510954:0.000000 +:@0.346497:0.527235:0.357074:0.527235:0.357074:0.510954:0.346497:0.510954:0.000000 +:@0.410631:0.527235:0.421208:0.527235:0.421208:0.510954:0.410631:0.510954:0.000000 +:@0.441148:0.527235:0.451724:0.527235:0.451724:0.510954:0.441148:0.510954:0.000000 +:@0.489157:0.527235:0.499733:0.527235:0.499733:0.510954:0.489157:0.510954:0.000000 +:@0.521657:0.527235:0.532234:0.527235:0.532234:0.510954:0.521657:0.510954:0.000000 =:@0.222468:0.526599:0.233275:0.526599:0.233275:0.510101:0.222468:0.510101:0.000000 ,:@0.252733:0.526599:0.255488:0.526599:0.255488:0.510101:0.252733:0.510101:0.000000 ,:@0.330199:0.526599:0.332954:0.526599:0.332954:0.510101:0.330199:0.510101:0.000000 =:@0.378940:0.526599:0.389748:0.526599:0.389748:0.510101:0.378940:0.510101:0.000000 ,:@0.473645:0.526599:0.476400:0.526599:0.476400:0.510101:0.473645:0.510101:0.000000 ,:@0.560126:0.526599:0.562881:0.526599:0.562881:0.510101:0.560126:0.510101:0.000000 :@0.108233:0.551706:0.112375:0.551706:0.112375:0.535208:0.108233:0.535208:0.000000 (:@0.161213:0.554641:0.167628:0.554641:0.167628:0.532662:0.161213:0.532662:0.000000 ) (:@0.213672:0.554641:0.241703:0.554641:0.241703:0.532662:0.213672:0.532662:0.000000:0.000000:0.000000 ):@0.282083:0.554641:0.288498:0.554641:0.288498:0.532662:0.282083:0.532662:0.000000 (:@0.336738:0.554641:0.343154:0.554641:0.343154:0.532662:0.336738:0.532662:0.000000 ):@0.469129:0.554641:0.475544:0.554641:0.475544:0.532662:0.469129:0.532662:0.000000 +:@0.148335:0.552342:0.158912:0.552342:0.158912:0.536061:0.148335:0.536061:0.000000 +:@0.182415:0.552342:0.192992:0.552342:0.192992:0.536061:0.182415:0.536061:0.000000 +:@0.256490:0.552342:0.267067:0.552342:0.267067:0.536061:0.256490:0.536061:0.000000 +:@0.290570:0.552342:0.301147:0.552342:0.301147:0.536061:0.290570:0.536061:0.000000 ++:@0.355591:0.552342:0.389979:0.552342:0.389979:0.536061:0.355591:0.536061:0.000000:0.000000 ++:@0.419667:0.552342:0.456059:0.552342:0.456059:0.536061:0.419667:0.536061:0.000000:0.000000 U:@0.133828:0.551821:0.145773:0.551821:0.145773:0.535352:0.133828:0.535352:0.000000 V W:@0.167908:0.551821:0.211583:0.551821:0.211583:0.535352:0.167908:0.535352:0.000000:0.000000:0.000000 U V:@0.241983:0.551821:0.280109:0.551821:0.280109:0.535352:0.241983:0.535352:0.000000:0.000000:0.000000 W:@0.303440:0.551821:0.319738:0.551821:0.319738:0.535352:0.303440:0.535352:0.000000 ac pb dq:@0.344282:0.551821:0.468373:0.551821:0.468373:0.535352:0.344282:0.535352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.222464:0.551706:0.233272:0.551706:0.233272:0.535208:0.222464:0.535208:0.000000 =:@0.323915:0.551706:0.334723:0.551706:0.334723:0.535208:0.323915:0.535208:0.000000 ,:@0.404174:0.551706:0.406929:0.551706:0.406929:0.535208:0.404174:0.535208:0.000000 .:@0.476515:0.551706:0.479270:0.551706:0.479270:0.535208:0.476515:0.535208:0.000000 :@0.108233:0.576814:0.112375:0.576814:0.112375:0.560316:0.108233:0.560316:0.000000 Conclusión:@0.131680:0.577277:0.218161:0.577277:0.218161:0.560331:0.131680:0.560331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : :@0.218161:0.576814:0.225058:0.576814:0.225058:0.560316:0.218161:0.560316:0.000000:0.000000 (:@0.254589:0.579749:0.261004:0.579749:0.261004:0.557770:0.254589:0.557770:0.000000 ) (:@0.307048:0.579749:0.335079:0.579749:0.335079:0.557770:0.307048:0.557770:0.000000:0.000000:0.000000 ):@0.375459:0.579749:0.381874:0.579749:0.381874:0.557770:0.375459:0.557770:0.000000 +:@0.241711:0.577450:0.252288:0.577450:0.252288:0.561169:0.241711:0.561169:0.000000 +:@0.275791:0.577450:0.286368:0.577450:0.286368:0.561169:0.275791:0.561169:0.000000 +:@0.349866:0.577450:0.360443:0.577450:0.360443:0.561169:0.349866:0.561169:0.000000 +:@0.383947:0.577450:0.394523:0.577450:0.394523:0.561169:0.383947:0.561169:0.000000 U:@0.227204:0.576930:0.239149:0.576930:0.239149:0.560461:0.227204:0.560461:0.000000 V W:@0.261285:0.576930:0.304959:0.576930:0.304959:0.560461:0.261285:0.560461:0.000000:0.000000:0.000000 U V:@0.335360:0.576930:0.373497:0.576930:0.373497:0.560461:0.335360:0.560461:0.000000:0.000000:0.000000 W:@0.396827:0.576930:0.413126:0.576930:0.413126:0.560461:0.396827:0.560461:0.000000 =:@0.315836:0.576814:0.326644:0.576814:0.326644:0.560316:0.315836:0.560316:0.000000 .:@0.414840:0.576814:0.417595:0.576814:0.417595:0.560316:0.414840:0.560316:0.000000 iii) Existencia del elemento neutro. :@0.108233:0.601509:0.365618:0.601509:0.365618:0.584795:0.108233:0.584795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El elemento O = (0, 0) pertenece :@0.365367:0.601292:0.599931:0.601292:0.599931:0.584795:0.365367:0.584795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.595760:0.601292:0.599903:0.601292:0.599903:0.584795:0.595760:0.584795:0.000000 a , donde 0:@0.131680:0.618643:0.228956:0.618643:0.228956:0.602145:0.131680:0.602145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.143663:0.617674:0.157572:0.617674:0.157572:0.604227:0.143663:0.604227:0.000000 2:@0.157579:0.612290:0.162532:0.612290:0.162532:0.602672:0.157579:0.602672:0.000000 :@0.228956:0.618426:0.245004:0.618426:0.245004:0.603779:0.228956:0.603779:0.000000 R:@0.245005:0.617674:0.258914:0.617674:0.258914:0.604227:0.245005:0.604227:0.000000 es el elemento neutro.:@0.258914:0.618643:0.419585:0.618643:0.419585:0.602145:0.258914:0.602145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Entonces,:@0.131688:0.643628:0.199692:0.643628:0.199692:0.627130:0.131688:0.627130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.260321:0.647420:0.266737:0.647420:0.266737:0.625930:0.260321:0.625930:0.000000 ) (:@0.293303:0.647420:0.320294:0.647420:0.320294:0.625930:0.293303:0.625930:0.000000:0.000000:0.000000 ) (:@0.346861:0.647420:0.375837:0.647420:0.375837:0.625930:0.346861:0.625930:0.000000:0.000000:0.000000 ):@0.449199:0.647420:0.455614:0.647420:0.455614:0.625930:0.449199:0.625930:0.000000 +:@0.219643:0.644386:0.230220:0.644386:0.230220:0.628105:0.219643:0.628105:0.000000 +:@0.301366:0.644386:0.311943:0.644386:0.311943:0.628105:0.301366:0.628105:0.000000 +:@0.387011:0.644386:0.397588:0.644386:0.397588:0.628105:0.387011:0.628105:0.000000 +:@0.427160:0.644386:0.437737:0.644386:0.437737:0.628105:0.427160:0.628105:0.000000 =:@0.247023:0.643750:0.257831:0.643750:0.257831:0.627252:0.247023:0.627252:0.000000 ,:@0.277328:0.643750:0.280082:0.643750:0.280082:0.627252:0.277328:0.627252:0.000000 0, 0=:@0.321002:0.643750:0.366950:0.643750:0.366950:0.627252:0.321002:0.627252:0.000000:0.000000:0.000000:0.000000:0.000000 0,:@0.399951:0.643750:0.412608:0.643750:0.412608:0.627252:0.399951:0.627252:0.000000:0.000000 0. :@0.440095:0.643750:0.467641:0.643620:0.467641:0.627122:0.440095:0.627252:0.000000:0.000000:0.000000:0.000000 UO:@0.205980:0.643866:0.244067:0.643866:0.244067:0.627397:0.205980:0.627397:0.000000:0.000000 ab:@0.267436:0.643866:0.293040:0.643866:0.293040:0.627397:0.267436:0.627397:0.000000:0.000000 a:@0.376535:0.643866:0.385513:0.643866:0.385513:0.627397:0.376535:0.627397:0.000000 b:@0.416279:0.643866:0.425546:0.643866:0.425546:0.627397:0.416279:0.627397:0.000000 :@0.108233:0.668104:0.112292:0.668104:0.112292:0.651606:0.108233:0.651606:0.000000 Como + 0 = , + 0 = se sigue que :@0.131681:0.668104:0.378270:0.668104:0.378270:0.651606:0.131681:0.651606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.178598:0.668220:0.187396:0.668220:0.187396:0.651751:0.178598:0.651751:0.000000 a b:@0.220927:0.668220:0.244716:0.668220:0.244716:0.651751:0.220927:0.651751:0.000000:0.000000:0.000000 b :@0.280625:0.668220:0.294766:0.668220:0.294766:0.651751:0.280625:0.651751:0.000000:0.000000:0.000000 (:@0.428169:0.671816:0.434393:0.671816:0.434393:0.650964:0.428169:0.650964:0.000000 ) (:@0.505576:0.671816:0.533691:0.671816:0.533691:0.650964:0.505576:0.650964:0.000000:0.000000:0.000000 ):@0.559468:0.671816:0.565693:0.671816:0.565693:0.650964:0.559468:0.650964:0.000000 +:@0.388700:0.668872:0.398963:0.668872:0.398963:0.653075:0.388700:0.653075:0.000000 +:@0.445246:0.668872:0.455509:0.668872:0.455509:0.653075:0.445246:0.653075:0.000000 +:@0.484203:0.668872:0.494465:0.668872:0.494465:0.653075:0.484203:0.653075:0.000000 =:@0.415263:0.668255:0.425749:0.668255:0.425749:0.652247:0.415263:0.652247:0.000000 0,:@0.457789:0.668255:0.470052:0.668255:0.470052:0.652247:0.457789:0.652247:0.000000:0.000000 0 =:@0.496746:0.668255:0.525047:0.668255:0.525047:0.652247:0.496746:0.652247:0.000000:0.000000:0.000000 ,:@0.543964:0.668255:0.546637:0.668255:0.546637:0.652247:0.543964:0.652247:0.000000 =.:@0.568468:0.668255:0.595629:0.668255:0.595629:0.652247:0.568468:0.652247:0.000000:0.000000 UO:@0.375445:0.668367:0.412400:0.668367:0.412400:0.652387:0.375445:0.652387:0.000000:0.000000 a:@0.435077:0.668367:0.443788:0.668367:0.443788:0.652387:0.435077:0.652387:0.000000 b:@0.473641:0.668367:0.482632:0.668367:0.482632:0.652387:0.473641:0.652387:0.000000 ab:@0.534374:0.668367:0.559217:0.668367:0.559217:0.652387:0.534374:0.652387:0.000000:0.000000 U:@0.580958:0.668367:0.592547:0.668367:0.592547:0.652387:0.580958:0.652387:0.000000 :@0.108233:0.694468:0.112375:0.694468:0.112375:0.677971:0.108233:0.677971:0.000000 Conclusión:@0.131679:0.694931:0.218161:0.694931:0.218161:0.677985:0.131679:0.677985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : :@0.218161:0.694468:0.225058:0.694468:0.225058:0.677971:0.218161:0.677971:0.000000:0.000000 ∈:@0.240041:0.695105:0.253777:0.695105:0.253777:0.678824:0.240041:0.678824:0.000000 O:@0.225226:0.694584:0.237132:0.694584:0.237132:0.678115:0.225226:0.678115:0.000000 2:@0.268416:0.686433:0.273334:0.686433:0.273334:0.676884:0.268416:0.676884:0.000000 es tal que para todo :@0.274479:0.694468:0.425054:0.694468:0.425054:0.677971:0.274479:0.677971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∈:@0.439443:0.695105:0.453179:0.695105:0.453179:0.678824:0.439443:0.678824:0.000000 U:@0.424628:0.694584:0.436572:0.694584:0.436572:0.678115:0.424628:0.678115:0.000000 2:@0.467817:0.686433:0.472734:0.686433:0.472734:0.676884:0.467817:0.676884:0.000000 , :@0.473449:0.694468:0.480346:0.694468:0.480346:0.677971:0.473449:0.677971:0.000000:0.000000 ∈:@0.146460:0.714341:0.160196:0.714341:0.160196:0.698060:0.146460:0.698060:0.000000 +:@0.203582:0.714341:0.214158:0.714341:0.214158:0.698060:0.203582:0.698060:0.000000 U:@0.131645:0.713821:0.143589:0.713821:0.143589:0.697352:0.131645:0.697352:0.000000 U OU:@0.189074:0.713821:0.256464:0.713821:0.256464:0.697352:0.189074:0.697352:0.000000:0.000000:0.000000:0.000000 ,:@0.183160:0.713705:0.185915:0.713705:0.185915:0.697207:0.183160:0.697207:0.000000 = .:@0.231689:0.713705:0.259624:0.713705:0.259624:0.697207:0.231689:0.697207:0.000000:0.000000:0.000000 2:@0.174836:0.705669:0.179753:0.705669:0.179753:0.696121:0.174836:0.696121:0.000000 :@0.108233:0.738183:0.112375:0.738183:0.112375:0.721686:0.108233:0.721686:0.000000 De manera similar, se prueba que :@0.131680:0.738183:0.370451:0.738183:0.370451:0.721686:0.131680:0.721686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.387522:0.738820:0.398099:0.738820:0.398099:0.722539:0.387522:0.722539:0.000000 OU U:@0.373016:0.738299:0.439982:0.738299:0.439982:0.721830:0.373016:0.721830:0.000000:0.000000:0.000000:0.000000 =.:@0.415206:0.738183:0.443141:0.738183:0.443141:0.721686:0.415206:0.721686:0.000000:0.000000 iv) Existencia de opuestos aditivos.:@0.108233:0.764765:0.366382:0.764765:0.366382:0.748050:0.108233:0.748050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dado :@0.366215:0.764548:0.416228:0.764548:0.416228:0.748050:0.366215:0.748050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.449432:0.768218:0.455848:0.768218:0.455848:0.746728:0.449432:0.746728:0.000000 ):@0.482415:0.768218:0.488830:0.768218:0.488830:0.746728:0.482415:0.746728:0.000000 ∈:@0.492099:0.765184:0.505835:0.765184:0.505835:0.748903:0.492099:0.748903:0.000000 =:@0.436134:0.764548:0.446941:0.764548:0.446941:0.748050:0.436134:0.748050:0.000000 ,:@0.466438:0.764548:0.469193:0.764548:0.469193:0.748050:0.466438:0.748050:0.000000 2:@0.524138:0.756512:0.529056:0.756512:0.529056:0.746963:0.524138:0.746963:0.000000 U:@0.421268:0.764663:0.433213:0.764663:0.433213:0.748195:0.421268:0.748195:0.000000 a b:@0.456562:0.764663:0.482147:0.764663:0.482147:0.748195:0.456562:0.748195:0.000000:0.000000:0.000000 y como :@0.532853:0.764548:0.599925:0.764548:0.599925:0.748050:0.532853:0.748050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.595773:0.764548:0.599915:0.764548:0.599915:0.748050:0.595773:0.748050:0.000000 a b:@0.131686:0.782014:0.153323:0.782014:0.153323:0.765545:0.131686:0.765545:0.000000:0.000000:0.000000 , :@0.140296:0.781899:0.146866:0.781899:0.146866:0.765401:0.140296:0.765401:0.000000:0.000000 :@0.153134:0.781682:0.168861:0.781682:0.168861:0.767035:0.153134:0.767035:0.000000 R:@0.168672:0.780930:0.182304:0.780930:0.182304:0.767483:0.168672:0.767483:0.000000 , por la existencia de opuestos aditivos en , existen – , –:@0.182114:0.781899:0.553936:0.781899:0.553936:0.765401:0.182114:0.765401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.453721:0.780930:0.467352:0.780930:0.467352:0.767483:0.453721:0.767483:0.000000 a b:@0.531091:0.782014:0.562828:0.782014:0.562828:0.765545:0.531091:0.765545:0.000000:0.000000:0.000000 :@0.562639:0.781682:0.578366:0.781682:0.578366:0.767035:0.562639:0.767035:0.000000 R:@0.578178:0.780930:0.591809:0.780930:0.591809:0.767483:0.578178:0.767483:0.000000 , :@0.591622:0.781899:0.599834:0.781899:0.599834:0.765401:0.591622:0.765401:0.000000:0.000000:0.000000 tal que :@0.131686:0.801135:0.183624:0.801135:0.183624:0.784638:0.131686:0.784638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.210602:0.802813:0.245645:0.802813:0.245645:0.780834:0.210602:0.780834:0.000000:0.000000:0.000000 +−:@0.197724:0.800514:0.228722:0.800514:0.228722:0.784233:0.197724:0.784233:0.000000:0.000000 a:@0.186416:0.799994:0.195393:0.799994:0.195393:0.783525:0.186416:0.783525:0.000000 a:@0.229705:0.799994:0.238682:0.799994:0.238682:0.783525:0.229705:0.783525:0.000000 =0, :@0.248026:0.799878:0.279525:0.801136:0.279525:0.784638:0.248026:0.783380:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.310895:0.802813:0.345939:0.802813:0.345939:0.780834:0.310895:0.780834:0.000000:0.000000:0.000000 +−:@0.298016:0.800514:0.329014:0.800514:0.329014:0.784233:0.298016:0.784233:0.000000:0.000000 b:@0.286283:0.799994:0.295550:0.799994:0.295550:0.783525:0.286283:0.783525:0.000000 b:@0.329572:0.799994:0.338839:0.799994:0.338839:0.783525:0.329572:0.783525:0.000000 =0. Definimos =:@0.348318:0.799878:0.484249:0.801135:0.484249:0.784638:0.348318:0.783380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.486266:0.804070:0.492681:0.804070:0.492681:0.782091:0.486266:0.782091:0.000000 ):@0.540555:0.804070:0.546971:0.804070:0.546971:0.782091:0.540555:0.782091:0.000000 −−:@0.493805:0.801771:0.530042:0.801771:0.530042:0.785491:0.493805:0.785491:0.000000:0.000000 ∈:@0.549346:0.801771:0.563082:0.801771:0.563082:0.785491:0.549346:0.785491:0.000000 V:@0.458626:0.801251:0.469376:0.801251:0.469376:0.784782:0.458626:0.784782:0.000000 a b:@0.505383:0.801251:0.539868:0.801251:0.539868:0.784782:0.505383:0.784782:0.000000:0.000000:0.000000 ,:@0.515266:0.801135:0.518021:0.801135:0.518021:0.784638:0.515266:0.784638:0.000000 . . :@0.585315:0.801135:0.590486:0.801135:0.590486:0.784638:0.585315:0.784638:0.000000:0.000000:0.000000:0.000000 2:@0.577724:0.793100:0.582642:0.793100:0.582642:0.783551:0.577724:0.783551:0.000000 Entonces:@0.131683:0.827003:0.195335:0.827003:0.195335:0.810505:0.131683:0.810505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.378639:0.831796:0.384926:0.831796:0.384926:0.806744:0.378639:0.806744:0.000000 ):@0.508186:0.831796:0.514474:0.831796:0.514474:0.806744:0.508186:0.806744:0.000000 ( ) (:@0.252776:0.829979:0.310535:0.829979:0.310535:0.808437:0.252776:0.808437:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.357457:0.829979:0.363744:0.829979:0.363744:0.808437:0.357457:0.808437:0.000000 ( ):@0.409741:0.829979:0.444086:0.829979:0.444086:0.808437:0.409741:0.808437:0.000000:0.000000:0.000000 ( ) ( ):@0.473561:0.829979:0.564779:0.829979:0.564779:0.808437:0.473561:0.808437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.213063:0.827725:0.223429:0.827725:0.223429:0.811769:0.213063:0.811769:0.000000 + −−:@0.291611:0.827725:0.347143:0.827725:0.347143:0.811769:0.291611:0.811769:0.000000:0.000000:0.000000:0.000000 +−:@0.397104:0.827725:0.427484:0.827725:0.427484:0.811769:0.397104:0.811769:0.000000:0.000000 +−:@0.460924:0.827725:0.491305:0.827725:0.491305:0.811769:0.460924:0.811769:0.000000:0.000000 UV:@0.198850:0.827215:0.236217:0.827215:0.236217:0.811074:0.198850:0.811074:0.000000:0.000000 ab:@0.260164:0.827215:0.282633:0.827215:0.282633:0.811074:0.260164:0.811074:0.000000:0.000000 ab:@0.322965:0.827215:0.356782:0.827215:0.356782:0.811074:0.322965:0.811074:0.000000:0.000000 a:@0.386030:0.827215:0.394829:0.827215:0.394829:0.811074:0.386030:0.811074:0.000000 a b:@0.428457:0.827215:0.458536:0.827215:0.458536:0.811074:0.428457:0.811074:0.000000:0.000000:0.000000 b:@0.491881:0.827215:0.500963:0.827215:0.500963:0.811074:0.491881:0.811074:0.000000 O:@0.580078:0.827215:0.591747:0.827215:0.591747:0.811074:0.580078:0.811074:0.000000 =:@0.240206:0.827102:0.250798:0.827102:0.250798:0.810932:0.240206:0.810932:0.000000 ,:@0.269869:0.827102:0.272569:0.827102:0.272569:0.810932:0.269869:0.810932:0.000000 ,:@0.332670:0.827102:0.335370:0.827102:0.335370:0.810932:0.332670:0.810932:0.000000 =:@0.366072:0.827102:0.376665:0.827102:0.376665:0.810932:0.366072:0.810932:0.000000 ,:@0.445750:0.827102:0.448450:0.827102:0.448450:0.810932:0.445750:0.810932:0.000000 = 0,0= .:@0.516821:0.827102:0.594888:0.827102:0.594888:0.810932:0.516821:0.810932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.108233:0.852107:0.112375:0.852107:0.112375:0.835610:0.108233:0.835610:0.000000 Conclusión:@0.131679:0.852570:0.218160:0.852570:0.218160:0.835624:0.131679:0.835624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : dado =( ,):@0.218160:0.852107:0.330702:0.852107:0.330702:0.835610:0.218160:0.835610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∈:@0.333531:0.852744:0.347267:0.852744:0.347267:0.836463:0.333531:0.836463:0.000000 U:@0.268299:0.852223:0.280243:0.852223:0.280243:0.835754:0.268299:0.835754:0.000000 a b:@0.302321:0.852223:0.325266:0.852223:0.325266:0.835754:0.302321:0.835754:0.000000:0.000000:0.000000 , existe =:@0.364994:0.852107:0.443567:0.853365:0.443567:0.836867:0.364994:0.835610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.445584:0.856300:0.452000:0.856300:0.452000:0.834321:0.445584:0.834321:0.000000 ):@0.499874:0.856300:0.506289:0.856300:0.506289:0.834321:0.499874:0.834321:0.000000 −−:@0.453123:0.854001:0.489361:0.854001:0.489361:0.837720:0.453123:0.837720:0.000000:0.000000 ∈:@0.508665:0.854001:0.522401:0.854001:0.522401:0.837720:0.508665:0.837720:0.000000 V:@0.417945:0.853480:0.428695:0.853480:0.428695:0.837012:0.417945:0.837012:0.000000 a b:@0.464701:0.853480:0.499186:0.853480:0.499186:0.837012:0.464701:0.837012:0.000000:0.000000:0.000000 ,:@0.474585:0.853365:0.477339:0.853365:0.477339:0.836867:0.474585:0.836867:0.000000 2:@0.537041:0.845329:0.541958:0.845329:0.541958:0.835780:0.537041:0.835780:0.000000 , tal :@0.541949:0.852107:0.570982:0.852107:0.570982:0.835610:0.541949:0.835610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que :@0.131696:0.869458:0.162848:0.869458:0.162848:0.852961:0.131696:0.852961:0.000000:0.000000:0.000000:0.000000 +:@0.179486:0.870094:0.190063:0.870094:0.190063:0.853814:0.179486:0.853814:0.000000 UV O:@0.164979:0.869574:0.232331:0.869574:0.232331:0.853105:0.164979:0.853105:0.000000:0.000000:0.000000:0.000000 =.:@0.207189:0.869458:0.235548:0.869458:0.235548:0.852961:0.207189:0.852961:0.000000:0.000000 Ejercicios resueltos:@0.108233:0.894313:0.238888:0.894313:0.238888:0.877526:0.108233:0.877526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. :@0.108233:0.918633:0.135762:0.918633:0.135762:0.901918:0.108233:0.901918:0.000000:0.000000:0.000000:0.000000 Sean = (2, 3), = (4, –1), = (8, –10). Entonces,:@0.131678:0.918416:0.491320:0.918416:0.491320:0.901918:0.131678:0.901918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 U:@0.169476:0.918532:0.181421:0.918532:0.181421:0.902063:0.169476:0.902063:0.000000 V:@0.243205:0.918532:0.253955:0.918532:0.253955:0.902063:0.243205:0.902063:0.000000 W:@0.326238:0.918532:0.342536:0.918532:0.342536:0.902063:0.326238:0.902063:0.000000 U+V+W:@0.131681:0.935882:0.189718:0.935882:0.189718:0.919413:0.131681:0.919413:0.000000:0.000000:0.000000:0.000000:0.000000 = (2,–3) + (4,–1) + (8,–10) = (2 + 4 + 8, –3–1–10) = (14, –14).:@0.189341:0.935767:0.595637:0.935767:0.595637:0.919269:0.189341:0.919269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.684804:0.104916:0.782426:0.104916:0.782426:0.089444:0.684804:0.089444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática:@0.684804:0.117484:0.768866:0.117484:0.768866:0.102012:0.684804:0.102012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Propiedades de la :@0.685042:0.142157:0.807677:0.142157:0.807677:0.126896:0.685042:0.126896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 adición de números reales:@0.638498:0.157999:0.814205:0.157999:0.814205:0.142738:0.638498:0.142738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i) Conmutativa :@0.638498:0.181194:0.751514:0.181194:0.751514:0.165722:0.638498:0.165722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : para todo :@0.745323:0.180772:0.823440:0.180772:0.823440:0.165708:0.745323:0.165708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y :@0.638498:0.196719:0.662421:0.196719:0.662421:0.181683:0.638498:0.181683:0.000000:0.000000:0.000000:0.000000 , :@0.645323:0.196614:0.651621:0.196614:0.651621:0.181550:0.645323:0.181550:0.000000:0.000000  :@0.662421:0.196416:0.681471:0.196416:0.681471:0.183042:0.662421:0.183042:0.000000:0.000000 R:@0.681470:0.195729:0.694170:0.195729:0.694170:0.183452:0.681470:0.183452:0.000000 , + = + .:@0.694170:0.196614:0.782964:0.196614:0.782964:0.181550:0.694170:0.181550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y y x:@0.700467:0.196719:0.780449:0.196719:0.780449:0.181683:0.700467:0.181683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ii) Asociativa:@0.638498:0.220007:0.729999:0.220007:0.729999:0.204535:0.638498:0.204535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : para todo :@0.730001:0.219584:0.808222:0.219584:0.808222:0.204521:0.730001:0.204521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y, z :@0.638498:0.235532:0.674733:0.235532:0.674733:0.220495:0.638498:0.220495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.645322:0.235426:0.651620:0.235426:0.651620:0.220363:0.645322:0.220363:0.000000:0.000000  :@0.674733:0.235228:0.693783:0.235228:0.693783:0.221855:0.674733:0.221855:0.000000:0.000000 R:@0.693783:0.234542:0.706483:0.234542:0.706483:0.222264:0.693783:0.222264:0.000000 , :@0.706483:0.235426:0.716562:0.235426:0.716562:0.220363:0.706483:0.220363:0.000000:0.000000:0.000000 x:@0.638498:0.251374:0.645322:0.251374:0.645322:0.236337:0.638498:0.236337:0.000000 + ( + ) = (:@0.645322:0.251268:0.727010:0.251268:0.727010:0.236205:0.645322:0.236205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y z:@0.668189:0.251374:0.698708:0.251374:0.698708:0.236337:0.668189:0.236337:0.000000:0.000000:0.000000 x + y + z.:@0.727010:0.251374:0.790335:0.251374:0.790335:0.236337:0.727010:0.236337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.758356:0.251268:0.763791:0.251268:0.763791:0.236205:0.758356:0.236205:0.000000 :@0.790335:0.251268:0.794116:0.251268:0.794116:0.236205:0.790335:0.236205:0.000000 iii) Existencia del elemento :@0.638498:0.274662:0.820181:0.274662:0.820181:0.259189:0.638498:0.259189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 neutro :@0.638498:0.290504:0.690195:0.290504:0.690195:0.275031:0.638498:0.275031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : existe 0 :@0.684003:0.290081:0.738655:0.290081:0.738655:0.275018:0.684003:0.275018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.738303:0.289883:0.757001:0.289883:0.757001:0.276510:0.738303:0.276510:0.000000:0.000000 R:@0.756650:0.289197:0.769350:0.289197:0.769350:0.276919:0.756650:0.276919:0.000000 , tal que :@0.768998:0.290081:0.821135:0.290081:0.821135:0.275018:0.768998:0.275018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para todo :@0.638498:0.305923:0.706905:0.305923:0.706905:0.290860:0.638498:0.290860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.638498:0.321871:0.645322:0.321871:0.645322:0.306834:0.638498:0.306834:0.000000 :@0.644971:0.321765:0.648752:0.321765:0.648752:0.306702:0.644971:0.306702:0.000000  :@0.648401:0.321567:0.667099:0.321567:0.667099:0.308194:0.648401:0.308194:0.000000:0.000000 R:@0.666748:0.320881:0.679448:0.320881:0.679448:0.308603:0.666748:0.308603:0.000000 , + 0 = 0 + = . :@0.679096:0.321765:0.790722:0.321765:0.790722:0.306702:0.679096:0.306702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.684690:0.321871:0.691515:0.321871:0.691515:0.306834:0.684690:0.306834:0.000000 x x:@0.755103:0.321871:0.784777:0.321871:0.784777:0.306834:0.755103:0.306834:0.000000:0.000000:0.000000 iv) Existencia de opuestos :@0.638498:0.345159:0.825336:0.345159:0.825336:0.329686:0.638498:0.329686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aditivos:@0.638498:0.361001:0.693837:0.361001:0.693837:0.345528:0.638498:0.345528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 : para cada :@0.693837:0.360578:0.777108:0.360578:0.777108:0.345515:0.693837:0.345515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.766851:0.360684:0.773676:0.360684:0.773676:0.345647:0.766851:0.345647:0.000000  :@0.776756:0.360380:0.795454:0.360380:0.795454:0.347007:0.776756:0.347007:0.000000:0.000000 R:@0.795101:0.359694:0.807801:0.359694:0.807801:0.347416:0.795101:0.347416:0.000000 , :@0.807450:0.360578:0.817529:0.360578:0.817529:0.345515:0.807450:0.345515:0.000000:0.000000:0.000000 existe – :@0.638498:0.376420:0.698427:0.376420:0.698427:0.361357:0.638498:0.361357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.688172:0.376526:0.694997:0.376526:0.694997:0.361489:0.688172:0.361489:0.000000  :@0.698075:0.376222:0.716773:0.376222:0.716773:0.362849:0.698075:0.362849:0.000000:0.000000 R:@0.716422:0.375536:0.729122:0.375536:0.729122:0.363258:0.716422:0.363258:0.000000 , tal que :@0.728770:0.376420:0.787503:0.376420:0.787503:0.361357:0.728770:0.361357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.638498:0.392368:0.645323:0.392368:0.645323:0.377331:0.638498:0.377331:0.000000 + (– ) = 0.:@0.645323:0.392262:0.717741:0.392262:0.717741:0.377199:0.645323:0.377199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.677777:0.392368:0.684602:0.392368:0.684602:0.377331:0.677777:0.377331:0.000000 Debido a la propiedad asociati-:@0.638498:0.415233:0.841167:0.415233:0.841167:0.400170:0.638498:0.400170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 va de la operación “+” en , :@0.638498:0.431075:0.827503:0.431075:0.827503:0.416012:0.638498:0.416012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.804724:0.430191:0.817424:0.430191:0.817424:0.417913:0.804724:0.417913:0.000000 se escribe + + en vez de :@0.638498:0.446917:0.832179:0.446917:0.832179:0.431854:0.638498:0.431854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.704934:0.447023:0.759709:0.447023:0.759709:0.431986:0.704934:0.431986:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.638498:0.462865:0.645323:0.462865:0.645323:0.447828:0.638498:0.447828:0.000000 + ( + ) o de ( + ) + :@0.645323:0.462759:0.816685:0.462759:0.816685:0.447696:0.645323:0.447696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y z:@0.668190:0.462865:0.698709:0.462865:0.698709:0.447828:0.668190:0.447828:0.000000:0.000000:0.000000 x y:@0.745938:0.462865:0.777213:0.462865:0.777213:0.447828:0.745938:0.447828:0.000000:0.000000:0.000000 z.:@0.800080:0.462865:0.809122:0.462865:0.809122:0.447828:0.800080:0.447828:0.000000:0.000000 El elemento neutro es único. :@0.638498:0.478601:0.826165:0.478601:0.826165:0.463538:0.638498:0.463538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Igualmente, dado que :@0.638498:0.494443:0.783737:0.494443:0.783737:0.479380:0.638498:0.479380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.783737:0.494549:0.794344:0.494549:0.794344:0.479512:0.783737:0.479512:0.000000:0.000000  :@0.794344:0.494245:0.813394:0.494245:0.813394:0.480872:0.794344:0.480872:0.000000:0.000000 R:@0.813395:0.493559:0.826095:0.493559:0.826095:0.481281:0.813395:0.481281:0.000000 , :@0.826095:0.494443:0.836174:0.494443:0.836174:0.479380:0.826095:0.479380:0.000000:0.000000:0.000000 el opuesto aditivo – es único.:@0.638498:0.510285:0.834695:0.510285:0.834695:0.495222:0.638498:0.495222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.768013:0.510391:0.774838:0.510391:0.774838:0.495354:0.768013:0.495354:0.000000 Sean = ( , ), = ( , ) :@0.638498:0.533256:0.801469:0.533256:0.801469:0.518193:0.638498:0.518193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A :@0.673009:0.533362:0.687081:0.533362:0.687081:0.518325:0.673009:0.518325:0.000000:0.000000 a b B:@0.706166:0.533362:0.749244:0.533362:0.749244:0.518325:0.706166:0.518325:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.772111:0.533362:0.792252:0.533362:0.792252:0.518325:0.772111:0.518325:0.000000:0.000000:0.000000 :@0.801469:0.533058:0.816122:0.533058:0.816122:0.519685:0.801469:0.519685:0.000000 R:@0.816122:0.532371:0.828822:0.532371:0.828822:0.520094:0.816122:0.520094:0.000000 2:@0.828824:0.527450:0.833346:0.527450:0.833346:0.518669:0.828824:0.518669:0.000000 . :@0.833345:0.533250:0.839643:0.533250:0.839643:0.518187:0.833345:0.518187:0.000000:0.000000 Diremos que es igual a , que :@0.638501:0.549092:0.844848:0.549092:0.844848:0.534029:0.638501:0.534029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.725798:0.549197:0.736088:0.549197:0.736088:0.534161:0.725798:0.534161:0.000000 B:@0.801717:0.549197:0.810107:0.549197:0.810107:0.534161:0.801717:0.534161:0.000000 se escribe = , si y solo si :@0.638501:0.564934:0.818760:0.564934:0.818760:0.549871:0.638501:0.549871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.704937:0.565039:0.741049:0.565039:0.741049:0.550003:0.704937:0.550003:0.000000:0.000000:0.000000:0.000000 a x b y:@0.638501:0.580881:0.718571:0.580881:0.718571:0.565845:0.638501:0.565845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = y = , es decir, :@0.646698:0.580776:0.783177:0.580776:0.783177:0.565713:0.646698:0.565713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B :@0.638501:0.596723:0.678395:0.596723:0.678395:0.581687:0.638501:0.581687:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.652573:0.596618:0.666223:0.596618:0.666223:0.581555:0.652573:0.581555:0.000000:0.000000 ⇔:@0.678395:0.597119:0.696724:0.597119:0.696724:0.579918:0.678395:0.579918:0.000000 a = x b = y:@0.696724:0.596723:0.783443:0.596723:0.783443:0.581687:0.696724:0.581687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ^:@0.736811:0.597872:0.746679:0.597872:0.746679:0.582809:0.736811:0.582809:0.000000 .:@0.783443:0.596618:0.785958:0.596618:0.785958:0.581555:0.783443:0.581555:0.000000 ©:@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