208:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
M.5.2.18. Realizar las operaciones de adición entre elementos de :@0.144797:0.943701:0.427221:0.943701:0.427221:0.933659:0.144797:0.933659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.427866:0.943111:0.436333:0.943111:0.436333:0.934926:0.427866:0.934926:0.000000
3:@0.436361:0.939834:0.439376:0.939834:0.439376:0.933980:0.436361:0.933980:0.000000
 y de producto por un número escalar de manera geométrica y analítica, aplicando propiedades de los :@0.439376:0.943701:0.894237:0.943701:0.894237:0.933659:0.439376:0.933659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números reales; y reconocer los vectores como elementos geométricos de  .:@0.144802:0.954262:0.479037:0.954262:0.479037:0.944220:0.144802:0.944220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.465885:0.953672:0.474352:0.953672:0.474352:0.945487:0.465885:0.945487:0.000000
3:@0.474345:0.950395:0.477360:0.950395:0.477360:0.944541:0.474345:0.944541:0.000000
M.5.2.19. Calcular el producto escalar entre dos vectores y la norma de un vector para determinar la distancia entre dos puntos A y B en R3, como la norma del vector AB.:@0.144792:0.963063:0.877022:0.963063:0.877022:0.953021:0.144792:0.953021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Operaciones en :@0.404235:0.120895:0.597775:0.120895:0.597775:0.076235:0.404235:0.076235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.597775:0.118895:0.634061:0.118895:0.634061:0.083817:0.597775:0.083817:0.000000
3:@0.634039:0.102029:0.642243:0.102029:0.642243:0.075992:0.634039:0.075992:0.000000
Saberes previos:@0.199646:0.106444:0.307805:0.106444:0.307805:0.090971:0.199646:0.090971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué operaciones se :@0.199884:0.135071:0.337434:0.135071:0.337434:0.120008:0.199884:0.120008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pueden efectuar en  ?:@0.153341:0.150913:0.305204:0.150913:0.305204:0.135850:0.153341:0.135850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.283651:0.149911:0.295746:0.149911:0.295746:0.138218:0.283651:0.138218:0.000000
3:@0.295578:0.145113:0.300101:0.145113:0.300101:0.136331:0.295578:0.136331:0.000000
Desequilibrio cognitivo:@0.199646:0.198065:0.363493:0.198065:0.363493:0.182592:0.199646:0.182592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Las propiedades de la :@0.199884:0.226692:0.348533:0.226692:0.348533:0.211629:0.199884:0.211629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adición de los números reales se :@0.153341:0.242534:0.365230:0.242534:0.365230:0.227471:0.153341:0.227471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cumplen para  ?:@0.153341:0.258376:0.268917:0.258376:0.268917:0.243313:0.153341:0.243313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.247363:0.257373:0.259459:0.257373:0.259459:0.245680:0.247363:0.245680:0.000000
3:@0.259291:0.252577:0.263814:0.252577:0.263814:0.243795:0.259291:0.243795:0.000000
Tal como en el estudio del espacio vectorial  , definiremos en   las :@0.404236:0.143953:0.895906:0.143953:0.895906:0.127455:0.404236:0.127455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.716154:0.142866:0.729459:0.142866:0.729459:0.130004:0.716154:0.130004:0.000000
2:@0.729459:0.137600:0.734412:0.137600:0.734412:0.127982:0.729459:0.127982:0.000000
R:@0.851389:0.142866:0.864694:0.142866:0.864694:0.130004:0.851389:0.130004:0.000000
3:@0.864694:0.137600:0.869647:0.137600:0.869647:0.127982:0.864694:0.127982:0.000000
operaciones de adición “+”, y de producto de números reales por ele-:@0.404238:0.160682:0.891855:0.160682:0.891855:0.144184:0.404238:0.144184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mentos de  . Con estas dos operaciones, obtendremos la estructura :@0.404238:0.177411:0.895940:0.177397:0.895940:0.160899:0.404238:0.160913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.483755:0.176310:0.497060:0.176310:0.497060:0.163448:0.483755:0.163448:0.000000
3:@0.497058:0.171044:0.502011:0.171044:0.502011:0.161426:0.497058:0.161426:0.000000
de espacio vertical, denominado espacio vertical :@0.404240:0.194126:0.758501:0.194126:0.758501:0.177628:0.404240:0.177628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.759950:0.193032:0.773255:0.193032:0.773255:0.180170:0.759950:0.180170:0.000000
3:@0.773255:0.187766:0.778208:0.187766:0.778208:0.178148:0.773255:0.178148:0.000000
 o simplemente :@0.778208:0.194119:0.895898:0.194119:0.895898:0.177621:0.778208:0.177621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
espacio  .:@0.404231:0.210848:0.482600:0.210841:0.482600:0.194344:0.404231:0.194350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.461588:0.209754:0.474893:0.209754:0.474893:0.196892:0.461588:0.196892:0.000000
3:@0.474893:0.204488:0.479846:0.204488:0.479846:0.194870:0.474893:0.194870:0.000000
Adición en :@0.404236:0.244929:0.495119:0.244929:0.495119:0.227246:0.404236:0.227246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.495119:0.243435:0.509634:0.243435:0.509634:0.229403:0.495119:0.229403:0.000000
3:@0.509634:0.238099:0.515342:0.238099:0.515342:0.227790:0.509634:0.227790:0.000000
Definición :@0.404236:0.261470:0.491103:0.261470:0.491103:0.244524:0.404236:0.244524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean   = ( ,  ,  ),   = ( ,  ,  ) dos elementos de :@0.484322:0.261008:0.847027:0.261008:0.847027:0.244510:0.484322:0.244510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.532119:0.261123:0.541328:0.261123:0.541328:0.244654:0.532119:0.244654:0.000000
:@0.535067:0.261499:0.541482:0.261499:0.541482:0.245681:0.535067:0.245681:0.000000
a b c v:@0.569802:0.261123:0.634552:0.261123:0.634552:0.244654:0.569802:0.244654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.628773:0.261499:0.635188:0.261499:0.635188:0.245681:0.628773:0.245681:0.000000
x y z:@0.663508:0.261123:0.702366:0.261123:0.702366:0.244654:0.663508:0.244654:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.848647:0.259921:0.861952:0.259921:0.861952:0.247058:0.848647:0.247058:0.000000
3:@0.861950:0.254654:0.866903:0.254654:0.866903:0.245036:0.861950:0.245036:0.000000
. Se :@0.866904:0.261008:0.895917:0.261008:0.895917:0.244510:0.866904:0.244510:0.000000:0.000000:0.000000:0.000000:0.000000
define la suma de   con  , que se escribe   +  , como sigue::@0.404229:0.277737:0.825503:0.277737:0.825503:0.261239:0.404229:0.261239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.533363:0.277852:0.542571:0.277852:0.542571:0.261383:0.533363:0.261383:0.000000
:@0.536312:0.278228:0.542727:0.278228:0.542727:0.262410:0.536312:0.262410:0.000000
v:@0.577964:0.277852:0.585747:0.277852:0.585747:0.261383:0.577964:0.261383:0.000000
:@0.579967:0.278228:0.586382:0.278228:0.586382:0.262410:0.579967:0.262410:0.000000
u v:@0.697192:0.277852:0.733434:0.277852:0.733434:0.261383:0.697192:0.261383:0.000000:0.000000:0.000000
:@0.700144:0.278228:0.706559:0.278228:0.706559:0.262410:0.700144:0.262410:0.000000
:@0.727655:0.278228:0.734070:0.278228:0.734070:0.262410:0.727655:0.262410:0.000000
u v:@0.485124:0.311296:0.521362:0.311296:0.521362:0.294827:0.485124:0.294827:0.000000:0.000000:0.000000
:@0.488072:0.311672:0.494487:0.311672:0.494487:0.295854:0.488072:0.295854:0.000000
 +   = ( ,  ,  ) + ( ,  ,  ) = (  +  ,   +  ,   +  ).:@0.494487:0.311180:0.810881:0.311180:0.810881:0.294682:0.494487:0.294682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.515583:0.311672:0.521998:0.311672:0.521998:0.295854:0.515583:0.295854:0.000000
a b c:@0.547043:0.311296:0.586267:0.311296:0.586267:0.294827:0.547043:0.294827:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.617265:0.311296:0.652867:0.311296:0.652867:0.294827:0.617265:0.294827:0.000000:0.000000:0.000000:0.000000:0.000000
a x b y c z:@0.683865:0.311296:0.802173:0.311296:0.802173:0.294827:0.683865:0.294827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404229:0.327909:0.408372:0.327909:0.408372:0.311411:0.404229:0.311411:0.000000
La definición expresa que la adición de dos elementos de   se realiza :@0.404229:0.344638:0.895912:0.344618:0.895912:0.328120:0.404229:0.328140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.807761:0.343531:0.821066:0.343531:0.821066:0.330669:0.807761:0.330669:0.000000
3:@0.821066:0.338265:0.826019:0.338265:0.826019:0.328647:0.821066:0.328647:0.000000
sumando sus respectivos componentes. El resultado es otro elemen-:@0.404244:0.361347:0.891822:0.361347:0.891822:0.344849:0.404244:0.344849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to de  .:@0.404244:0.378076:0.466918:0.378062:0.466918:0.361565:0.404244:0.361578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.445906:0.376975:0.459211:0.376975:0.459211:0.364113:0.445906:0.364113:0.000000
3:@0.459211:0.371709:0.464164:0.371709:0.464164:0.362091:0.459211:0.362091:0.000000
Ejercicios resueltos:@0.404229:0.411882:0.534884:0.411882:0.534884:0.395095:0.404229:0.395095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404229:0.428452:0.416501:0.428452:0.416501:0.411737:0.404229:0.411737:0.000000:0.000000
  Sean   = (–5, 8, 10),   = (3; –5,5; –4). Entonces,:@0.416501:0.428235:0.757147:0.428235:0.757147:0.411737:0.416501:0.411737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.465762:0.428351:0.474971:0.428351:0.474971:0.411882:0.465762:0.411882:0.000000
:@0.468709:0.428726:0.475125:0.428726:0.475125:0.412908:0.468709:0.412908:0.000000
v:@0.571297:0.428351:0.579080:0.428351:0.579080:0.411882:0.571297:0.411882:0.000000
:@0.573301:0.428726:0.579716:0.428726:0.579716:0.412908:0.573301:0.412908:0.000000
u v:@0.427963:0.445080:0.464201:0.445080:0.464201:0.428611:0.427963:0.428611:0.000000:0.000000:0.000000
:@0.430911:0.445455:0.437326:0.445455:0.437326:0.429637:0.430911:0.429637:0.000000
 +   = (–5, 8, 10) + (3; –5,5; –4):@0.437326:0.444964:0.656642:0.444964:0.656642:0.428466:0.437326:0.428466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.458422:0.445455:0.464837:0.445455:0.464837:0.429637:0.458422:0.429637:0.000000
 :@0.404229:0.461693:0.408371:0.461693:0.408371:0.445195:0.404229:0.445195:0.000000
 :@0.427973:0.461693:0.432115:0.461693:0.432115:0.445195:0.427973:0.445195:0.000000
= (–5 + 3; 8 – 5,5; –10 –4) = (–2; 2,5; –14).:@0.469557:0.461693:0.768226:0.461693:0.768226:0.445195:0.469557:0.445195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.404229:0.495353:0.416501:0.495353:0.416501:0.478639:0.404229:0.478639:0.000000:0.000000
  Dado       se definen   = ( , – ,  ),   = (– ,  , – )    . Entonces, :@0.416501:0.495136:0.895921:0.495117:0.895921:0.478619:0.416501:0.478639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.470135:0.495252:0.479113:0.495252:0.479113:0.478783:0.470135:0.478783:0.000000
:@0.482193:0.494598:0.496846:0.494598:0.496846:0.481225:0.482193:0.481225:0.000000
R:@0.499914:0.494030:0.513219:0.494030:0.513219:0.481168:0.499914:0.481168:0.000000
,:@0.513070:0.494796:0.515585:0.494796:0.515585:0.479733:0.513070:0.479733:0.000000
u:@0.592724:0.495233:0.601933:0.495233:0.601933:0.478764:0.592724:0.478764:0.000000
:@0.595518:0.495609:0.601933:0.495609:0.601933:0.479790:0.595518:0.479790:0.000000
a a a v:@0.624666:0.495233:0.692499:0.495233:0.692499:0.478764:0.624666:0.478764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.686565:0.495609:0.692980:0.495609:0.692980:0.479790:0.686565:0.479790:0.000000
a a a:@0.726059:0.495233:0.774636:0.495233:0.774636:0.478764:0.726059:0.478764:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.783448:0.494598:0.798101:0.494598:0.798101:0.481225:0.783448:0.481225:0.000000
R:@0.801169:0.494030:0.814474:0.494030:0.814474:0.481168:0.801169:0.481168:0.000000
3:@0.814326:0.488764:0.819280:0.488764:0.819280:0.479146:0.814326:0.479146:0.000000
u v:@0.427970:0.511962:0.463226:0.511962:0.463226:0.495493:0.427970:0.495493:0.000000:0.000000:0.000000
:@0.430821:0.512338:0.437237:0.512338:0.437237:0.496519:0.430821:0.496519:0.000000
 +   = ( , – ,  ) + (– ,  , – ) = ( –  , –  +  ,  –  ) = (0, 0, 0) = 0.:@0.437140:0.511846:0.891704:0.511846:0.891704:0.495348:0.437140:0.495348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.457350:0.512338:0.463765:0.512338:0.463765:0.496519:0.457350:0.496519:0.000000
a a a:@0.487827:0.511962:0.537878:0.511962:0.537878:0.495493:0.487827:0.495493:0.000000:0.000000:0.000000:0.000000:0.000000
a a a:@0.578201:0.511962:0.628252:0.511962:0.628252:0.495493:0.578201:0.495493:0.000000:0.000000:0.000000:0.000000:0.000000
a  a a a a  a:@0.658171:0.511962:0.789155:0.511962:0.789155:0.495493:0.658171:0.495493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.882630:0.511080:0.889046:0.511080:0.889046:0.495262:0.882630:0.495262:0.000000
 :@0.404178:0.545290:0.408320:0.545290:0.408320:0.528792:0.404178:0.528792:0.000000
La definición de suma de elementos de :@0.427912:0.545290:0.716367:0.545290:0.716367:0.528792:0.427912:0.528792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.717466:0.544196:0.730771:0.544196:0.730771:0.531334:0.717466:0.531334:0.000000
3:@0.730771:0.538930:0.735724:0.538930:0.735724:0.529312:0.730771:0.529312:0.000000
 muestra que la suma :@0.735723:0.545283:0.895921:0.545283:0.895921:0.528786:0.735723:0.528786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de dos elementos de   es otro elemento de  . Más aún, la ope-:@0.427979:0.562012:0.891749:0.562005:0.891749:0.545508:0.427979:0.545515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.579810:0.560918:0.593114:0.560918:0.593114:0.548056:0.579810:0.548056:0.000000
3:@0.593114:0.555652:0.598068:0.555652:0.598068:0.546034:0.593114:0.546034:0.000000
R:@0.749153:0.560918:0.762458:0.560918:0.762458:0.548056:0.749153:0.548056:0.000000
3:@0.762458:0.555652:0.767411:0.555652:0.767411:0.546034:0.762458:0.546034:0.000000
ración adición en :@0.427977:0.578734:0.557266:0.578734:0.557266:0.562237:0.427977:0.562237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.558475:0.577641:0.571780:0.577641:0.571780:0.564778:0.558475:0.564778:0.000000
3:@0.571780:0.572374:0.576733:0.572374:0.576733:0.562756:0.571780:0.562756:0.000000
 es una ley de composición interna, esto es, :@0.576732:0.578727:0.895881:0.578727:0.895881:0.562230:0.576732:0.562230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
“+” es una función de   ×   en   definida como sigue: :@0.427985:0.595456:0.839675:0.595450:0.839675:0.578952:0.427985:0.578959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.584988:0.594363:0.598293:0.594363:0.598293:0.581500:0.584988:0.581500:0.000000
3:@0.598293:0.589097:0.603246:0.589097:0.603246:0.579478:0.598293:0.579478:0.000000
R:@0.622337:0.594363:0.635642:0.594363:0.635642:0.581500:0.622337:0.581500:0.000000
3:@0.635642:0.589097:0.640595:0.589097:0.640595:0.579478:0.635642:0.579478:0.000000
R:@0.666430:0.594363:0.679734:0.594363:0.679734:0.581500:0.666430:0.581500:0.000000
3:@0.679734:0.589097:0.684688:0.589097:0.684688:0.579478:0.679734:0.579478:0.000000
+::@0.522956:0.628893:0.536519:0.628893:0.536519:0.612395:0.522956:0.612395:0.000000:0.000000
donde  +   está arriba definido. Se tiene así la propiedad clausu-:@0.427979:0.669465:0.891819:0.669465:0.891819:0.652967:0.427979:0.652967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.479166:0.669581:0.488375:0.669581:0.488375:0.653112:0.479166:0.653112:0.000000
:@0.482114:0.669957:0.488529:0.669957:0.488529:0.654139:0.482114:0.654139:0.000000
v:@0.507929:0.669581:0.515712:0.669581:0.515712:0.653112:0.507929:0.653112:0.000000
:@0.509933:0.669957:0.516348:0.669957:0.516348:0.654139:0.509933:0.654139:0.000000
rativa que se expresa del modo siguiente::@0.427998:0.686194:0.718533:0.686194:0.718533:0.669696:0.427998:0.669696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.555815:0.727218:0.567388:0.727218:0.567388:0.708219:0.555815:0.708219:0.000000
u v:@0.567396:0.719748:0.591439:0.719748:0.591439:0.703279:0.567396:0.703279:0.000000:0.000000:0.000000
 :@0.570344:0.720124:0.592075:0.720124:0.592075:0.704305:0.570344:0.704305:0.000000:0.000000:0.000000
,           +      .:@0.576759:0.719632:0.740191:0.719632:0.740191:0.703134:0.576759:0.703134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.596061:0.719113:0.610714:0.719113:0.610714:0.705740:0.596061:0.705740:0.000000
R:@0.614561:0.718545:0.627866:0.718545:0.627866:0.705683:0.614561:0.705683:0.000000
3:@0.627718:0.713279:0.632671:0.713279:0.632671:0.703661:0.627718:0.703661:0.000000
⇒:@0.636660:0.719126:0.655675:0.719126:0.655675:0.701414:0.636660:0.701414:0.000000
u v:@0.659817:0.719748:0.696055:0.719748:0.696055:0.703279:0.659817:0.703279:0.000000:0.000000:0.000000
:@0.662764:0.720124:0.669180:0.720124:0.669180:0.704305:0.662764:0.704305:0.000000
:@0.690275:0.720124:0.696690:0.720124:0.696690:0.704305:0.690275:0.704305:0.000000
:@0.700827:0.719113:0.715480:0.719113:0.715480:0.705740:0.700827:0.705740:0.000000
R:@0.719327:0.718545:0.732632:0.718545:0.732632:0.705683:0.719327:0.705683:0.000000
3:@0.732483:0.713279:0.737436:0.713279:0.737436:0.703661:0.732483:0.703661:0.000000
Teorema :@0.404244:0.753538:0.477972:0.753538:0.477972:0.736592:0.404244:0.736592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. La operación “+” en   satisface las siguientes propiedades::@0.471190:0.753076:0.891793:0.753076:0.891793:0.736578:0.471190:0.736578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.620835:0.751989:0.634139:0.751989:0.634139:0.739127:0.620835:0.739127:0.000000
3:@0.634139:0.746723:0.639093:0.746723:0.639093:0.737105:0.634139:0.737105:0.000000
i.:@0.404230:0.786737:0.411840:0.786737:0.411840:0.770022:0.404230:0.770022:0.000000:0.000000
  Conmutativa: para todo  ,      ,   +   =   +  .:@0.411840:0.786520:0.771655:0.786520:0.771655:0.770023:0.411840:0.770022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.603874:0.786635:0.627919:0.786635:0.627919:0.770167:0.603874:0.770167:0.000000:0.000000:0.000000
 :@0.606824:0.787011:0.628555:0.787011:0.628555:0.771193:0.606824:0.771193:0.000000:0.000000:0.000000
:@0.632555:0.786002:0.647207:0.786002:0.647207:0.772628:0.632555:0.772628:0.000000
R:@0.651054:0.785433:0.664359:0.785433:0.664359:0.772571:0.651054:0.772571:0.000000
3:@0.664212:0.780169:0.669165:0.780169:0.669165:0.770550:0.664212:0.770550:0.000000
u v:@0.676061:0.786636:0.712299:0.786636:0.712299:0.770167:0.676061:0.770167:0.000000:0.000000:0.000000
:@0.679008:0.787012:0.685423:0.787012:0.685423:0.771194:0.679008:0.771194:0.000000
:@0.706519:0.787012:0.712934:0.787012:0.712934:0.771194:0.706519:0.771194:0.000000
v:@0.732026:0.786636:0.739809:0.786636:0.739809:0.770167:0.732026:0.770167:0.000000
:@0.734030:0.787012:0.740445:0.787012:0.740445:0.771194:0.734030:0.771194:0.000000
u:@0.759537:0.786636:0.768746:0.786636:0.768746:0.770167:0.759537:0.770167:0.000000
:@0.762485:0.787012:0.768900:0.787012:0.768900:0.771194:0.762485:0.771194:0.000000
ii.:@0.404247:0.820181:0.416114:0.820181:0.416114:0.803466:0.404247:0.803466:0.000000:0.000000:0.000000
  Asociativa: para todo  ,  ,       ,   + (  +  ) = (  +  ) +  .:@0.416114:0.819964:0.856787:0.819965:0.856787:0.803467:0.416114:0.803466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v w:@0.583067:0.820080:0.626857:0.820080:0.626857:0.803611:0.583067:0.803611:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.586015:0.820456:0.625566:0.820456:0.625566:0.804637:0.586015:0.804637:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.631918:0.819446:0.646570:0.819446:0.646570:0.806073:0.631918:0.806073:0.000000
R:@0.650418:0.818878:0.663722:0.818878:0.663722:0.806015:0.650418:0.806015:0.000000
3:@0.663573:0.813613:0.668527:0.813613:0.668527:0.803995:0.663573:0.803995:0.000000
u:@0.675424:0.820080:0.684633:0.820080:0.684633:0.803611:0.675424:0.803611:0.000000
:@0.678372:0.820456:0.684787:0.820456:0.684787:0.804638:0.678372:0.804638:0.000000
v:@0.709832:0.820080:0.717615:0.820080:0.717615:0.803611:0.709832:0.803611:0.000000
:@0.711835:0.820456:0.718251:0.820456:0.718251:0.804638:0.711835:0.804638:0.000000
w:@0.737343:0.820080:0.749557:0.820080:0.749557:0.803611:0.737343:0.803611:0.000000
:@0.741851:0.820456:0.748266:0.820456:0.748266:0.804638:0.741851:0.804638:0.000000
u v:@0.780227:0.820080:0.816465:0.820080:0.816465:0.803611:0.780227:0.803611:0.000000:0.000000:0.000000
:@0.783175:0.820456:0.789590:0.820456:0.789590:0.804638:0.783175:0.804638:0.000000
:@0.810685:0.820456:0.817101:0.820456:0.817101:0.804638:0.810685:0.804638:0.000000
w:@0.842146:0.820080:0.854360:0.820080:0.854360:0.803611:0.842146:0.803611:0.000000
:@0.846654:0.820456:0.853069:0.820456:0.853069:0.804638:0.846654:0.804638:0.000000
iii.:@0.404246:0.853625:0.420371:0.853625:0.420371:0.836910:0.404246:0.836910:0.000000:0.000000:0.000000:0.000000
  Existencia del elemento neutro:  existe 0     tal que para todo:@0.420371:0.853408:0.877958:0.853409:0.877958:0.836911:0.420371:0.836910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.702973:0.852642:0.709389:0.852642:0.709389:0.836824:0.702973:0.836824:0.000000
:@0.713430:0.852890:0.728083:0.852890:0.728083:0.839517:0.713430:0.839517:0.000000
R:@0.731930:0.852322:0.745235:0.852322:0.745235:0.839460:0.731930:0.839460:0.000000
3:@0.745087:0.847056:0.750040:0.847056:0.750040:0.837438:0.745087:0.837438:0.000000
 :@0.404228:0.870138:0.408370:0.870138:0.408370:0.853640:0.404228:0.853640:0.000000
u:@0.427963:0.870253:0.437171:0.870253:0.437171:0.853785:0.427963:0.853785:0.000000
:@0.430910:0.870629:0.437326:0.870629:0.437326:0.854811:0.430910:0.854811:0.000000
    ,   + 0 = 0 +   =  .:@0.437326:0.870138:0.607383:0.870131:0.607383:0.853633:0.437326:0.853640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.441483:0.869612:0.456136:0.869612:0.456136:0.856239:0.441483:0.856239:0.000000
R:@0.459983:0.869044:0.473288:0.869044:0.473288:0.856182:0.459983:0.856182:0.000000
3:@0.473140:0.863779:0.478094:0.863779:0.478094:0.854161:0.473140:0.854161:0.000000
u:@0.484991:0.870247:0.494200:0.870247:0.494200:0.853778:0.484991:0.853778:0.000000
:@0.487939:0.870622:0.494354:0.870622:0.494354:0.854804:0.487939:0.854804:0.000000
:@0.514717:0.869365:0.521133:0.869365:0.521133:0.853546:0.514717:0.853546:0.000000
:@0.541400:0.869365:0.547815:0.869365:0.547815:0.853546:0.541400:0.853546:0.000000
u u:@0.566811:0.870247:0.604474:0.870247:0.604474:0.853778:0.566811:0.853778:0.000000:0.000000:0.000000
:@0.569758:0.870622:0.576174:0.870622:0.576174:0.854804:0.569758:0.854804:0.000000
:@0.598213:0.870622:0.604628:0.870622:0.604628:0.854804:0.598213:0.854804:0.000000
iv.:@0.404231:0.903791:0.419431:0.903791:0.419431:0.887077:0.404231:0.887077:0.000000:0.000000:0.000000
  Existencia de opuestos aditivos: para cada      , existe       tal :@0.419431:0.903574:0.895921:0.903575:0.895921:0.887077:0.419431:0.887077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.723936:0.903690:0.733145:0.903690:0.733145:0.887221:0.723936:0.887221:0.000000
:@0.726847:0.904066:0.733262:0.904066:0.733262:0.888248:0.726847:0.888248:0.000000
:@0.736800:0.903056:0.751452:0.903056:0.751452:0.889683:0.736800:0.889683:0.000000
R:@0.754675:0.902488:0.767979:0.902488:0.767979:0.889626:0.754675:0.889626:0.000000
3:@0.767832:0.897223:0.772785:0.897223:0.772785:0.887605:0.767832:0.887605:0.000000
v:@0.822351:0.903691:0.830135:0.903691:0.830135:0.887222:0.822351:0.887222:0.000000
:@0.824338:0.904067:0.830753:0.904067:0.830753:0.888249:0.824338:0.888249:0.000000
:@0.834274:0.903056:0.848926:0.903056:0.848926:0.889683:0.834274:0.889683:0.000000
R:@0.852150:0.902488:0.865455:0.902488:0.865455:0.889626:0.852150:0.889626:0.000000
3:@0.865306:0.897223:0.870259:0.897223:0.870259:0.887605:0.865306:0.887605:0.000000
que   +   = 0.:@0.427987:0.920304:0.525450:0.920304:0.525450:0.903806:0.427987:0.903806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.459139:0.920420:0.495377:0.920420:0.495377:0.903951:0.459139:0.903951:0.000000:0.000000:0.000000
:@0.462086:0.920796:0.468502:0.920796:0.468502:0.904978:0.462086:0.904978:0.000000
:@0.489597:0.920796:0.496013:0.920796:0.496013:0.904978:0.489597:0.904978:0.000000
:@0.516376:0.919538:0.522791:0.919538:0.522791:0.903720:0.516376:0.903720:0.000000
R:@0.560811:0.621867:0.574116:0.621867:0.574116:0.609005:0.560811:0.609005:0.000000
3:@0.574114:0.616603:0.579067:0.616603:0.579067:0.606984:0.574114:0.606984:0.000000
 × :@0.579068:0.622954:0.598159:0.622954:0.598159:0.606457:0.579068:0.606457:0.000000:0.000000:0.000000
R:@0.598159:0.621867:0.611463:0.621867:0.611463:0.609005:0.598159:0.609005:0.000000
3 :@0.611463:0.616603:0.618831:0.616603:0.618831:0.606984:0.611463:0.606984:0.000000:0.000000
→:@0.618831:0.631053:0.634975:0.631053:0.634975:0.611190:0.618831:0.611190:0.000000
 :@0.634975:0.622954:0.639117:0.622954:0.639117:0.606457:0.634975:0.606457:0.000000
R:@0.639115:0.621867:0.652420:0.621867:0.652420:0.609005:0.639115:0.609005:0.000000
3:@0.652420:0.616603:0.657373:0.616603:0.657373:0.606984:0.652420:0.606984:0.000000
,:@0.657373:0.622634:0.659889:0.622634:0.659889:0.607571:0.657373:0.607571:0.000000
( ,  )     + :@0.560811:0.640305:0.650279:0.640305:0.650279:0.623807:0.560811:0.623807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.566764:0.640421:0.590807:0.640421:0.590807:0.623952:0.566764:0.623952:0.000000:0.000000:0.000000
 :@0.569711:0.640797:0.591443:0.640797:0.591443:0.624979:0.569711:0.624979:0.000000:0.000000:0.000000
→:@0.601538:0.648404:0.617682:0.648404:0.617682:0.628541:0.601538:0.628541:0.000000
u v:@0.621824:0.640421:0.658062:0.640421:0.658062:0.623952:0.621824:0.623952:0.000000:0.000000:0.000000
:@0.624771:0.640797:0.631187:0.640797:0.631187:0.624979:0.624771:0.624979:0.000000
:@0.652282:0.640797:0.658698:0.640797:0.658698:0.624979:0.652282:0.624979:0.000000
,:@0.658693:0.639984:0.661209:0.639984:0.661209:0.624921:0.658693:0.624921:0.000000
Competencia :@0.199644:0.408837:0.297267:0.408837:0.297267:0.393365:0.199644:0.393365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.421405:0.283707:0.421405:0.283707:0.405933:0.199644:0.405933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Estas son las propiedades :@0.199880:0.445880:0.365258:0.445880:0.365258:0.430817:0.199880:0.430817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la adición de números reales::@0.153337:0.461722:0.359876:0.461722:0.359876:0.446659:0.153337:0.446659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153337:0.485340:0.160426:0.485340:0.160426:0.469643:0.153337:0.469643:0.000000
  Conmutativa: para todo :@0.160426:0.484693:0.330572:0.484693:0.330572:0.469630:0.160426:0.469630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.169960:0.500640:0.190100:0.500640:0.190100:0.485604:0.169960:0.485604:0.000000:0.000000:0.000000
,   :@0.176785:0.500535:0.193882:0.500535:0.193882:0.485472:0.176785:0.485472:0.000000:0.000000:0.000000:0.000000
:@0.193886:0.500185:0.207841:0.500185:0.207841:0.487448:0.193886:0.487448:0.000000
 :@0.207841:0.500335:0.212239:0.500335:0.212239:0.486962:0.207841:0.486962:0.000000
R:@0.212239:0.499531:0.224334:0.499531:0.224334:0.487838:0.212239:0.487838:0.000000
,     +   =   +  .:@0.224332:0.500533:0.320690:0.500533:0.320690:0.485470:0.224332:0.485470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y y x:@0.238193:0.500639:0.318175:0.500639:0.318175:0.485602:0.238193:0.485602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153339:0.524151:0.160428:0.524151:0.160428:0.508454:0.153339:0.508454:0.000000
 :@0.160428:0.523504:0.164210:0.523504:0.164210:0.508441:0.160428:0.508441:0.000000
Asociativa: :@0.169961:0.523610:0.242149:0.523610:0.242149:0.508573:0.169961:0.508573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo:@0.242149:0.523504:0.306511:0.523504:0.306511:0.508441:0.242149:0.508441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.153339:0.539346:0.157121:0.539346:0.157121:0.524283:0.153339:0.524283:0.000000
x y z:@0.169961:0.539452:0.202468:0.539452:0.202468:0.524415:0.169961:0.524415:0.000000:0.000000:0.000000:0.000000:0.000000
,  ,   :@0.176786:0.539346:0.206250:0.539346:0.206250:0.524283:0.176786:0.524283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.206251:0.538997:0.220206:0.538997:0.220206:0.526261:0.206251:0.526261:0.000000
 :@0.220206:0.539148:0.224604:0.539148:0.224604:0.525775:0.220206:0.525775:0.000000
R:@0.224604:0.538344:0.236699:0.538344:0.236699:0.526651:0.224604:0.526651:0.000000
,:@0.236699:0.539346:0.239214:0.539346:0.239214:0.524283:0.236699:0.524283:0.000000
 :@0.153340:0.555188:0.157122:0.555188:0.157122:0.540125:0.153340:0.540125:0.000000
x:@0.169962:0.555294:0.176787:0.555294:0.176787:0.540257:0.169962:0.540257:0.000000
 + ( +  ) = (  +  ) +  .:@0.176787:0.555188:0.321201:0.555188:0.321201:0.540125:0.176787:0.540125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y  z:@0.199654:0.555294:0.230173:0.555294:0.230173:0.540257:0.199654:0.540257:0.000000:0.000000:0.000000:0.000000
x y   z:@0.258475:0.555294:0.318686:0.555294:0.318686:0.540257:0.258475:0.540257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153340:0.578806:0.160428:0.578806:0.160428:0.563109:0.153340:0.563109:0.000000
 :@0.160428:0.578159:0.164210:0.578159:0.164210:0.563096:0.160428:0.563096:0.000000
Existencia de elemento neutro: :@0.169962:0.578265:0.363926:0.578265:0.363926:0.563228:0.169962:0.563228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
existe 0 :@0.169962:0.594001:0.221587:0.594001:0.221587:0.578938:0.169962:0.578938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.221590:0.593651:0.235545:0.593651:0.235545:0.580915:0.221590:0.580915:0.000000
 :@0.235545:0.593802:0.239942:0.593802:0.239942:0.580429:0.235545:0.580429:0.000000
R:@0.239942:0.592997:0.252037:0.592997:0.252037:0.581304:0.239942:0.581304:0.000000
, tal que para :@0.252037:0.594000:0.339282:0.594000:0.339282:0.578937:0.252037:0.578937:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
todo   :@0.169962:0.609842:0.216418:0.609842:0.216418:0.594779:0.169962:0.594779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.205811:0.609948:0.212636:0.609948:0.212636:0.594911:0.205811:0.594911:0.000000
:@0.216418:0.609493:0.230373:0.609493:0.230373:0.596757:0.216418:0.596757:0.000000
 :@0.230373:0.609644:0.234771:0.609644:0.234771:0.596271:0.230373:0.596271:0.000000
R:@0.234771:0.608839:0.246866:0.608839:0.246866:0.597146:0.234771:0.597146:0.000000
,   + 0 = 0 +   =  .:@0.246866:0.609842:0.361394:0.609842:0.361394:0.594779:0.246866:0.594779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.253163:0.609948:0.259988:0.609948:0.259988:0.594911:0.253163:0.594911:0.000000
x x:@0.327798:0.609948:0.358879:0.609948:0.358879:0.594911:0.327798:0.594911:0.000000:0.000000:0.000000
•:@0.153340:0.633460:0.160428:0.633460:0.160428:0.617763:0.153340:0.617763:0.000000
 :@0.160428:0.632813:0.164210:0.632813:0.164210:0.617750:0.160428:0.617750:0.000000
Existencia de opuestos aditi-:@0.169962:0.632918:0.346074:0.632918:0.346074:0.617882:0.169962:0.617882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vos: :@0.169962:0.648760:0.197139:0.648760:0.197139:0.633724:0.169962:0.633724:0.000000:0.000000:0.000000:0.000000:0.000000
para cada   :@0.197139:0.648655:0.274463:0.648655:0.274463:0.633592:0.197139:0.633592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.263856:0.648760:0.270681:0.648760:0.270681:0.633724:0.263856:0.633724:0.000000
:@0.274464:0.648305:0.288418:0.648305:0.288418:0.635568:0.274464:0.635568:0.000000
 :@0.288418:0.648456:0.292816:0.648456:0.292816:0.635082:0.288418:0.635082:0.000000
R:@0.292816:0.647651:0.304911:0.647651:0.304911:0.635958:0.292816:0.635958:0.000000
, existe :@0.304911:0.648654:0.351296:0.648654:0.351296:0.633590:0.304911:0.633590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–  :@0.169961:0.664496:0.190154:0.664496:0.190154:0.649432:0.169961:0.649432:0.000000:0.000000:0.000000
x:@0.179547:0.664601:0.186372:0.664601:0.186372:0.649564:0.179547:0.649564:0.000000
:@0.190157:0.664147:0.204112:0.664147:0.204112:0.651410:0.190157:0.651410:0.000000
 :@0.204112:0.664297:0.208510:0.664297:0.208510:0.650924:0.204112:0.650924:0.000000
R:@0.208510:0.663493:0.220605:0.663493:0.220605:0.651800:0.208510:0.651800:0.000000
, tal que    + (– ) = 0.:@0.220605:0.664496:0.358581:0.664496:0.358581:0.649432:0.220605:0.649432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.279338:0.664601:0.286163:0.664601:0.286163:0.649564:0.279338:0.649564:0.000000
x:@0.318616:0.664601:0.325441:0.664601:0.325441:0.649564:0.318616:0.649564:0.000000