149:@0.918240:0.967835:0.943652:0.967835:0.943652:0.951847:0.918240:0.951847:0.000000:0.000000:0.000000
Producto de escalares por elementos de :@0.108231:0.094592:0.431176:0.094592:0.431176:0.076909:0.108231:0.076909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.431176:0.093098:0.445690:0.093098:0.445690:0.079067:0.431176:0.079067:0.000000
2:@0.445690:0.087762:0.451398:0.087762:0.451398:0.077453:0.445690:0.077453:0.000000
 :@0.451398:0.094592:0.455599:0.094592:0.455599:0.076909:0.451398:0.076909:0.000000
En lo sucesivo, a los elementos de   los denominamos escalares.:@0.108231:0.118427:0.564059:0.118427:0.564059:0.101929:0.108231:0.101929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.349506:0.117458:0.363416:0.117458:0.363416:0.104011:0.349506:0.104011:0.000000
Definición:@0.108228:0.143369:0.188316:0.143369:0.188316:0.126423:0.108228:0.126423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.108232:0.160257:0.146030:0.160257:0.146030:0.143759:0.108232:0.143759:0.000000:0.000000:0.000000:0.000000:0.000000
a :@0.146165:0.160373:0.159285:0.160373:0.159285:0.143904:0.146165:0.143904:0.000000:0.000000
 :@0.159420:0.160040:0.180284:0.160040:0.180284:0.145393:0.159420:0.145393:0.000000:0.000000
R:@0.180438:0.159289:0.194347:0.159289:0.194347:0.145842:0.180438:0.145842:0.000000
 y :@0.194347:0.160257:0.210588:0.160257:0.210588:0.143760:0.194347:0.143760:0.000000:0.000000:0.000000
U =  x, y:@0.210723:0.160373:0.270464:0.160373:0.270464:0.143904:0.210723:0.143904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.242106:0.160257:0.248059:0.160257:0.248059:0.143760:0.242106:0.143760:0.000000
) :@0.270464:0.160257:0.280559:0.160257:0.280559:0.143760:0.270464:0.143760:0.000000:0.000000
 :@0.280675:0.160041:0.301539:0.160041:0.301539:0.145394:0.280675:0.145394:0.000000:0.000000
R:@0.301693:0.159289:0.315603:0.159289:0.315603:0.145842:0.301693:0.145842:0.000000
2:@0.315588:0.153904:0.320541:0.153904:0.320541:0.144286:0.315588:0.144286:0.000000
. Se define el producto de   por U, que :@0.320541:0.160257:0.599941:0.160257:0.599941:0.143760:0.320541:0.143760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.507316:0.160373:0.516294:0.160373:0.516294:0.143904:0.507316:0.143904:0.000000
se escribe   .  , como sigue:   ∙ :@0.108238:0.177608:0.328554:0.177608:0.328554:0.161111:0.108238:0.161111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a U:@0.181001:0.177724:0.212962:0.177724:0.212962:0.161255:0.181001:0.161255:0.000000:0.000000:0.000000
a U = a  x, y:@0.308537:0.177724:0.407905:0.177724:0.407905:0.161255:0.308537:0.161255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∙ (:@0.372787:0.177608:0.385637:0.177608:0.385637:0.161111:0.372787:0.161111:0.000000:0.000000:0.000000
) = (:@0.407905:0.177608:0.438903:0.177608:0.438903:0.161111:0.407905:0.161111:0.000000:0.000000:0.000000:0.000000:0.000000
ax, ay:@0.438903:0.177724:0.479127:0.177724:0.479127:0.161255:0.438903:0.161255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
).:@0.479133:0.177608:0.487841:0.177608:0.487841:0.161111:0.479133:0.161111:0.000000:0.000000
De la definición, se sigue que el producto de un número real por un :@0.108238:0.202087:0.599887:0.202087:0.599887:0.185590:0.108238:0.185590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elemento de   es otro elemento de  , cuyos componentes son los :@0.108238:0.219438:0.599901:0.219437:0.599901:0.202940:0.108238:0.202940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.202021:0.218469:0.215931:0.218469:0.215931:0.205022:0.202021:0.205022:0.000000
2:@0.215928:0.213084:0.220881:0.213084:0.220881:0.203466:0.215928:0.203466:0.000000
R:@0.372036:0.218469:0.385946:0.218469:0.385946:0.205022:0.372036:0.205022:0.000000
2:@0.385958:0.213084:0.390911:0.213084:0.390911:0.203466:0.385958:0.203466:0.000000
productos del número real por los respectivos componentes del par :@0.108232:0.236788:0.599856:0.236788:0.599856:0.220290:0.108232:0.220290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ordenado.:@0.108232:0.254139:0.180226:0.254139:0.180226:0.237641:0.108232:0.237641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El producto de escalares (números reales) por pares ordenados de   :@0.108232:0.278618:0.599907:0.278617:0.599907:0.262120:0.108232:0.262120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.576975:0.277649:0.590885:0.277649:0.590885:0.264202:0.576975:0.264202:0.000000
2:@0.590813:0.272266:0.595766:0.272266:0.595766:0.262647:0.590813:0.262647:0.000000
es una operación a la que notamos “ ∙ ” y es una función de :@0.108238:0.295968:0.524514:0.295968:0.524514:0.279470:0.108238:0.279470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R  R:@0.524098:0.294999:0.569525:0.294999:0.569525:0.281552:0.524098:0.281552:0.000000:0.000000:0.000000:0.000000
×:@0.542333:0.294230:0.551731:0.294230:0.551731:0.279884:0.542333:0.279884:0.000000
   en :@0.551899:0.295968:0.599908:0.295968:0.599908:0.279470:0.551899:0.279470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.569534:0.289616:0.574487:0.289616:0.574487:0.279998:0.569534:0.279998:0.000000
R:@0.108230:0.312350:0.122139:0.312350:0.122139:0.298903:0.108230:0.298903:0.000000
2:@0.122141:0.306967:0.127094:0.306967:0.127094:0.297349:0.122141:0.297349:0.000000
 definida como sigue::@0.127093:0.313319:0.277938:0.313319:0.277938:0.296821:0.127093:0.296821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.296872:0.342614:0.299627:0.342614:0.299627:0.326116:0.296872:0.326116:0.000000
(, ):@0.313209:0.354514:0.349889:0.354519:0.349889:0.338022:0.313209:0.338016:0.000000:0.000000:0.000000:0.000000
,:@0.404410:0.354519:0.407164:0.354519:0.407164:0.338022:0.404410:0.338022:0.000000
2:@0.358961:0.324795:0.363879:0.324795:0.363879:0.315246:0.358961:0.315246:0.000000
2:@0.406184:0.324795:0.411102:0.324795:0.411102:0.315246:0.406184:0.315246:0.000000
⋅:@0.289648:0.343250:0.294464:0.343250:0.294464:0.326969:0.289648:0.326969:0.000000
×:@0.330534:0.333467:0.341111:0.333467:0.341111:0.317186:0.330534:0.317186:0.000000
→:@0.369007:0.333467:0.388022:0.333467:0.388022:0.317186:0.369007:0.317186:0.000000
→⋅:@0.352731:0.355155:0.390472:0.355155:0.390472:0.338875:0.352731:0.338875:0.000000:0.000000
aU:@0.319171:0.354635:0.344370:0.354635:0.344370:0.338166:0.319171:0.338166:0.000000:0.000000
aU:@0.375194:0.354635:0.403264:0.354635:0.403264:0.338166:0.375194:0.338166:0.000000:0.000000
con  ∙  arriba definido. Además, se asume que :@0.108236:0.381370:0.456329:0.381367:0.456329:0.364869:0.108236:0.364872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a   U:@0.139715:0.381485:0.172442:0.381482:0.172442:0.365014:0.139715:0.365016:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.469887:0.382015:0.472566:0.382015:0.472566:0.365973:0.469887:0.365973:0.000000
.:@0.512750:0.382015:0.515429:0.382015:0.515429:0.365973:0.512750:0.365973:0.000000
(,:@0.541713:0.382015:0.567959:0.382015:0.567959:0.365973:0.541713:0.365973:0.000000:0.000000
):@0.588705:0.382015:0.594494:0.382015:0.594494:0.365973:0.588705:0.365973:0.000000
aU Ua:@0.459655:0.382128:0.525860:0.382128:0.525860:0.366113:0.459655:0.366113:0.000000:0.000000:0.000000:0.000000:0.000000
ax ay:@0.547517:0.382128:0.588488:0.382128:0.588488:0.366113:0.547517:0.366113:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.488074:0.382634:0.457781:0.382634:0.457781:0.366802:0.488074:0.366802:0.000000
=:@0.528652:0.382634:0.498359:0.382634:0.498359:0.366802:0.528652:0.366802:0.000000
, :@0.593011:0.381366:0.599908:0.381366:0.599908:0.364869:0.593011:0.364869:0.000000:0.000000
 :@0.595765:0.381366:0.599908:0.381366:0.599908:0.364869:0.595765:0.364869:0.000000
donde :@0.108239:0.401609:0.159273:0.401609:0.159273:0.385111:0.108239:0.385111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.173686:0.400988:0.187422:0.400988:0.187422:0.384707:0.173686:0.384707:0.000000
a:@0.162069:0.400467:0.171047:0.400467:0.171047:0.383999:0.162069:0.383999:0.000000
, :@0.204311:0.401609:0.211208:0.401609:0.211208:0.385111:0.204311:0.385111:0.000000:0.000000
=:@0.228406:0.401239:0.238983:0.401239:0.238983:0.384959:0.228406:0.384959:0.000000
∈:@0.280654:0.401239:0.294390:0.401239:0.294390:0.384959:0.280654:0.384959:0.000000
U:@0.213172:0.400719:0.225116:0.400719:0.225116:0.384250:0.213172:0.384250:0.000000
x y:@0.249140:0.400719:0.271642:0.400719:0.271642:0.384250:0.249140:0.384250:0.000000:0.000000:0.000000
(, ):@0.242436:0.400603:0.277807:0.400603:0.277807:0.384105:0.242436:0.384105:0.000000:0.000000:0.000000:0.000000
2:@0.309027:0.392567:0.313945:0.392567:0.313945:0.383019:0.309027:0.383019:0.000000
. Siempre que no haya peligro de confu-:@0.315144:0.401609:0.595765:0.401609:0.595765:0.385111:0.315144:0.385111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sión, se escribirá :@0.108235:0.418960:0.226269:0.418960:0.226269:0.402462:0.108235:0.402462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aU:@0.226269:0.419075:0.247191:0.419075:0.247191:0.402607:0.226269:0.402607:0.000000:0.000000
 en lugar de :@0.247191:0.418960:0.334519:0.418960:0.334519:0.402462:0.247191:0.402462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.U.:@0.334519:0.419075:0.359968:0.419075:0.359968:0.402607:0.334519:0.402607:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.108235:0.443815:0.238890:0.443815:0.238890:0.427028:0.108235:0.427028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108235:0.466009:0.120507:0.466009:0.120507:0.449295:0.108235:0.449295:0.000000:0.000000
   Para :@0.120508:0.465793:0.166166:0.465793:0.166166:0.449295:0.120508:0.449295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.166170:0.467121:0.175585:0.467121:0.175585:0.450652:0.166170:0.450652:0.000000
=:@0.178250:0.467641:0.189343:0.467641:0.189343:0.451360:0.178250:0.451360:0.000000
2 y :@0.202958:0.467005:0.229427:0.467005:0.229427:0.450507:0.202958:0.450507:0.000000:0.000000:0.000000:0.000000
U:@0.229266:0.467121:0.241793:0.467121:0.241793:0.450652:0.229266:0.450652:0.000000
=:@0.244703:0.467641:0.255796:0.467641:0.255796:0.451360:0.244703:0.451360:0.000000
2 4:@0.279826:0.458164:0.307681:0.458164:0.307681:0.441666:0.279826:0.441666:0.000000:0.000000:0.000000
5 9:@0.279826:0.478363:0.307681:0.478363:0.307681:0.461865:0.279826:0.461865:0.000000:0.000000:0.000000
,:@0.292839:0.467005:0.295729:0.467005:0.295729:0.450507:0.292839:0.450507:0.000000
,:@0.319689:0.467005:0.322578:0.467005:0.322578:0.450507:0.319689:0.450507:0.000000
 se tiene:@0.327147:0.465787:0.385555:0.465787:0.385555:0.449289:0.327147:0.449289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108236:0.504537:0.112378:0.504537:0.112378:0.488039:0.108236:0.488039:0.000000
aU:@0.131685:0.507664:0.153188:0.507664:0.153188:0.491195:0.131685:0.491195:0.000000:0.000000
=:@0.156068:0.508184:0.167040:0.508184:0.167040:0.491903:0.156068:0.491903:0.000000
2:@0.187457:0.507548:0.196270:0.507548:0.196270:0.491050:0.187457:0.491050:0.000000
( ):@0.169699:0.511217:0.203554:0.511217:0.203554:0.489726:0.169699:0.489726:0.000000:0.000000:0.000000
2 4:@0.225636:0.498707:0.253175:0.498713:0.253175:0.482216:0.225636:0.482209:0.000000:0.000000:0.000000
5 9:@0.225636:0.518901:0.253185:0.518901:0.253185:0.502404:0.225636:0.502404:0.000000:0.000000:0.000000
,:@0.238506:0.507548:0.241364:0.507548:0.241364:0.491050:0.238506:0.491050:0.000000
=:@0.265714:0.508184:0.276686:0.508184:0.276686:0.491903:0.265714:0.491903:0.000000
2:@0.304869:0.507548:0.313683:0.507548:0.313683:0.491050:0.304869:0.491050:0.000000
( ):@0.287112:0.511217:0.320966:0.511217:0.320966:0.489726:0.287112:0.489726:0.000000:0.000000:0.000000
2:@0.343048:0.498707:0.351861:0.498707:0.351861:0.482209:0.343048:0.482209:0.000000
5:@0.343048:0.518901:0.351861:0.518901:0.351861:0.502404:0.343048:0.502404:0.000000
,:@0.363741:0.507548:0.366598:0.507548:0.366598:0.491050:0.363741:0.491050:0.000000
2:@0.387961:0.507548:0.396775:0.507548:0.396775:0.491050:0.387961:0.491050:0.000000
( ):@0.370202:0.511217:0.404056:0.511217:0.404056:0.489726:0.370202:0.489726:0.000000:0.000000:0.000000
4:@0.407020:0.498707:0.415834:0.498707:0.415834:0.482209:0.407020:0.482209:0.000000
9:@0.407020:0.518901:0.415834:0.518901:0.415834:0.502404:0.407020:0.502404:0.000000
=:@0.428365:0.508184:0.439336:0.508184:0.439336:0.491903:0.428365:0.491903:0.000000
4:@0.451767:0.498713:0.460580:0.498713:0.460580:0.482216:0.451767:0.482216:0.000000
5:@0.451553:0.518901:0.460367:0.518901:0.460367:0.502404:0.451553:0.502404:0.000000
,:@0.464642:0.507548:0.467500:0.507548:0.467500:0.491050:0.464642:0.491050:0.000000
8:@0.482073:0.498707:0.490886:0.498707:0.490886:0.482209:0.482073:0.482209:0.000000
9:@0.482291:0.518901:0.491104:0.518901:0.491104:0.502404:0.482291:0.502404:0.000000
.:@0.502223:0.507548:0.505080:0.507548:0.505080:0.491050:0.502223:0.491050:0.000000
2.:@0.108231:0.545374:0.120503:0.545374:0.120503:0.528660:0.108231:0.528660:0.000000:0.000000
  Sea :@0.120503:0.545158:0.159938:0.545158:0.159938:0.528660:0.120503:0.528660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(, ):@0.191357:0.545158:0.230448:0.545158:0.230448:0.528660:0.191357:0.528660:0.000000:0.000000:0.000000:0.000000
. . Como  ,:@0.269248:0.545158:0.338986:0.545158:0.338986:0.528660:0.269248:0.528660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.261665:0.537122:0.266582:0.537122:0.266582:0.527573:0.261665:0.527573:0.000000
=:@0.177327:0.545794:0.187903:0.545794:0.187903:0.529513:0.177327:0.529513:0.000000
∈:@0.233292:0.545794:0.247028:0.545794:0.247028:0.529513:0.233292:0.529513:0.000000
U:@0.162092:0.545273:0.174036:0.545273:0.174036:0.528804:0.162092:0.528804:0.000000
a b:@0.197328:0.545273:0.225012:0.545273:0.225012:0.528804:0.197328:0.528804:0.000000:0.000000:0.000000
y 0:@0.384818:0.545158:0.406030:0.545158:0.406030:0.528660:0.384818:0.528660:0.000000:0.000000:0.000000
0,0:@0.440977:0.545158:0.469065:0.545158:0.469065:0.528660:0.440977:0.528660:0.000000:0.000000:0.000000
0, entonces:@0.504013:0.545158:0.588207:0.545158:0.588207:0.528660:0.504013:0.528660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.352041:0.545794:0.365777:0.545794:0.365777:0.529513:0.352041:0.529513:0.000000
⋅ =:@0.408006:0.545794:0.437116:0.545794:0.437116:0.529513:0.408006:0.529513:0.000000:0.000000:0.000000
⋅ =:@0.471042:0.545794:0.500152:0.545794:0.500152:0.529513:0.471042:0.529513:0.000000:0.000000:0.000000
ab:@0.326338:0.545273:0.349263:0.545273:0.349263:0.528804:0.326338:0.528804:0.000000:0.000000
a:@0.414495:0.545273:0.423473:0.545273:0.423473:0.528804:0.414495:0.528804:0.000000
b:@0.477107:0.545273:0.486374:0.545273:0.486374:0.528804:0.477107:0.528804:0.000000
 :@0.108235:0.562508:0.112377:0.562508:0.112377:0.546011:0.108235:0.546011:0.000000
0:@0.134668:0.562508:0.143164:0.562508:0.143164:0.546011:0.134668:0.546011:0.000000
0 (, )(0:@0.180481:0.562508:0.265653:0.562508:0.265653:0.546011:0.180481:0.546011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, 0:@0.292085:0.562508:0.307324:0.562508:0.307324:0.546011:0.292085:0.546011:0.000000:0.000000:0.000000
) (0,0):@0.332176:0.562508:0.392326:0.562508:0.392326:0.546011:0.332176:0.546011:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.421975:0.562508:0.424730:0.562508:0.424730:0.546011:0.421975:0.546011:0.000000
⋅= ⋅:@0.145139:0.563144:0.195768:0.563144:0.195768:0.546864:0.145139:0.546864:0.000000:0.000000:0.000000:0.000000
=:@0.237188:0.563144:0.247765:0.563144:0.247765:0.546864:0.237188:0.546864:0.000000
×:@0.268475:0.563144:0.279051:0.563144:0.279051:0.546864:0.268475:0.546864:0.000000
×:@0.310146:0.563144:0.320722:0.563144:0.320722:0.546864:0.310146:0.546864:0.000000
=:@0.341403:0.563144:0.351980:0.563144:0.351980:0.546864:0.341403:0.546864:0.000000
=:@0.395596:0.563144:0.406173:0.563144:0.406173:0.546864:0.395596:0.546864:0.000000
U:@0.150793:0.562624:0.162737:0.562624:0.162737:0.546155:0.150793:0.546155:0.000000
a b:@0.202982:0.562624:0.228489:0.562624:0.228489:0.546155:0.202982:0.546155:0.000000:0.000000:0.000000
a:@0.282201:0.562624:0.291178:0.562624:0.291178:0.546155:0.282201:0.546155:0.000000
b:@0.323448:0.562624:0.332714:0.562624:0.332714:0.546155:0.323448:0.546155:0.000000
O:@0.409621:0.562624:0.421527:0.562624:0.421527:0.546155:0.409621:0.546155:0.000000
Conclusión:@0.131676:0.582208:0.218160:0.582208:0.218160:0.565262:0.131676:0.565262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: para todo :@0.218160:0.581745:0.299689:0.581745:0.299689:0.565247:0.218160:0.565247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,0:@0.353354:0.581745:0.371541:0.581745:0.371541:0.565247:0.353354:0.565247:0.000000:0.000000
.:@0.420783:0.581745:0.423537:0.581745:0.423537:0.565247:0.420783:0.565247:0.000000
2:@0.345030:0.573709:0.349947:0.573709:0.349947:0.564161:0.345030:0.564161:0.000000
∈:@0.316655:0.582381:0.330391:0.582381:0.330391:0.566100:0.316655:0.566100:0.000000
⋅ =:@0.373506:0.582381:0.404967:0.582381:0.404967:0.566100:0.373506:0.566100:0.000000:0.000000:0.000000
U:@0.301841:0.581861:0.313785:0.581861:0.313785:0.565392:0.301841:0.565392:0.000000
U O:@0.379171:0.581861:0.420334:0.581861:0.420334:0.565392:0.379171:0.565392:0.000000:0.000000:0.000000
3.:@0.108236:0.606817:0.120508:0.606817:0.120508:0.590102:0.108236:0.590102:0.000000:0.000000
  Sea  a:@0.120503:0.606601:0.170771:0.606601:0.170771:0.590103:0.120503:0.590103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.  Entonces :@0.202192:0.606601:0.281811:0.606601:0.281811:0.590103:0.202192:0.590103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.173757:0.607237:0.187493:0.607237:0.187493:0.590956:0.173757:0.590956:0.000000
(0,0)(:@0.347566:0.605595:0.407712:0.605595:0.407712:0.589097:0.347566:0.589097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0,:@0.432738:0.605595:0.445395:0.605595:0.445395:0.589097:0.432738:0.589097:0.000000:0.000000
0) (0,0):@0.474409:0.605595:0.542877:0.605595:0.542877:0.589097:0.474409:0.589097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.572527:0.605595:0.575282:0.605595:0.575282:0.589097:0.572527:0.589097:0.000000
⋅= ⋅:@0.295267:0.606231:0.346301:0.606231:0.346301:0.589950:0.295267:0.589950:0.000000:0.000000:0.000000:0.000000
=:@0.387721:0.606231:0.398297:0.606231:0.398297:0.589950:0.387721:0.589950:0.000000
×:@0.419008:0.606231:0.429584:0.606231:0.429584:0.589950:0.419008:0.589950:0.000000
×:@0.460678:0.606231:0.471255:0.606231:0.471255:0.589950:0.460678:0.589950:0.000000
=:@0.491950:0.606231:0.502527:0.606231:0.502527:0.589950:0.491950:0.589950:0.000000
=:@0.546143:0.606231:0.556720:0.606231:0.556720:0.589950:0.546143:0.589950:0.000000
aO a:@0.284791:0.605710:0.339986:0.605710:0.339986:0.589242:0.284791:0.589242:0.000000:0.000000:0.000000:0.000000
a:@0.407703:0.605710:0.416681:0.605710:0.416681:0.589242:0.407703:0.589242:0.000000
a:@0.449374:0.605710:0.458351:0.605710:0.458351:0.589242:0.449374:0.589242:0.000000
O:@0.560149:0.605710:0.572055:0.605710:0.572055:0.589242:0.560149:0.589242:0.000000
Conclusión :@0.131676:0.624414:0.224941:0.624414:0.224941:0.607468:0.131676:0.607468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: para todo :@0.218160:0.623951:0.299573:0.623951:0.299573:0.607454:0.218160:0.607454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.343343:0.623951:0.346098:0.623951:0.346098:0.607454:0.343343:0.607454:0.000000
.:@0.410039:0.623951:0.412794:0.623951:0.412794:0.607454:0.410039:0.607454:0.000000
∈:@0.314175:0.624588:0.327911:0.624588:0.327911:0.608307:0.314175:0.608307:0.000000
⋅ =:@0.362338:0.624588:0.394222:0.624588:0.394222:0.608307:0.362338:0.608307:0.000000:0.000000:0.000000
a:@0.302558:0.624067:0.311536:0.624067:0.311536:0.607598:0.302558:0.607598:0.000000
a OO:@0.351877:0.624067:0.409577:0.624067:0.409577:0.607598:0.351877:0.607598:0.000000:0.000000:0.000000:0.000000
Propiedades del producto de escalares por elementos de :@0.108231:0.651501:0.563812:0.651501:0.563812:0.633818:0.108231:0.633818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.563813:0.650007:0.578327:0.650007:0.578327:0.635976:0.563813:0.635976:0.000000
2:@0.578325:0.644671:0.584033:0.644671:0.584033:0.634362:0.578325:0.634362:0.000000
Teorema:@0.108231:0.675799:0.175176:0.675799:0.175176:0.658853:0.108231:0.658853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo :@0.108231:0.692687:0.182306:0.692687:0.182306:0.676189:0.108231:0.676189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a, b :@0.182633:0.692802:0.212023:0.692802:0.212023:0.676334:0.182633:0.676334:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.212350:0.692470:0.233214:0.692470:0.233214:0.677823:0.212350:0.677823:0.000000:0.000000
R:@0.233571:0.691718:0.247481:0.691718:0.247481:0.678271:0.233571:0.678271:0.000000
 y para todo :@0.247481:0.692687:0.339193:0.692687:0.339193:0.676189:0.247481:0.676189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U, V :@0.339492:0.692802:0.372782:0.692802:0.372782:0.676334:0.339492:0.676334:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.373109:0.692470:0.393974:0.692470:0.393974:0.677823:0.373109:0.677823:0.000000:0.000000
R:@0.394320:0.691718:0.408230:0.691718:0.408230:0.678271:0.394320:0.678271:0.000000
2:@0.408232:0.686335:0.413185:0.686335:0.413185:0.676717:0.408232:0.676717:0.000000
, se verifican las siguientes :@0.413185:0.692687:0.599931:0.692687:0.599931:0.676189:0.413185:0.676189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades::@0.108236:0.710037:0.199647:0.710037:0.199647:0.693540:0.108236:0.693540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.108236:0.728227:0.118774:0.728227:0.118774:0.711512:0.108236:0.711512:0.000000:0.000000
   (:@0.118774:0.728011:0.149364:0.726760:0.149364:0.710262:0.118774:0.711513:0.000000:0.000000:0.000000:0.000000
) ():@0.169689:0.726760:0.222399:0.726760:0.222399:0.710262:0.169689:0.710262:0.000000:0.000000:0.000000:0.000000
(:@0.260363:0.726760:0.266316:0.726760:0.266316:0.710262:0.260363:0.710262:0.000000
).:@0.286641:0.726760:0.295001:0.726760:0.295001:0.710262:0.286641:0.710262:0.000000:0.000000
=:@0.178909:0.727396:0.131208:0.727396:0.131208:0.711115:0.178909:0.711115:0.000000
=:@0.237186:0.727396:0.189486:0.727396:0.189486:0.711115:0.237186:0.711115:0.000000
abU:@0.134676:0.726875:0.170124:0.726875:0.170124:0.710406:0.134676:0.710406:0.000000:0.000000:0.000000
abU baU:@0.198906:0.726875:0.287083:0.726875:0.287083:0.710406:0.198906:0.710406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii):@0.108225:0.746207:0.123020:0.746207:0.123020:0.729492:0.108225:0.729492:0.000000:0.000000:0.000000
  (:@0.123027:0.745996:0.140202:0.744739:0.140202:0.728241:0.123027:0.729499:0.000000:0.000000:0.000000
):@0.173570:0.744739:0.179523:0.744739:0.179523:0.728241:0.173570:0.728241:0.000000
.:@0.266910:0.744739:0.269665:0.744739:0.269665:0.728241:0.266910:0.728241:0.000000
+:@0.151530:0.745375:0.162107:0.745375:0.162107:0.729094:0.151530:0.729094:0.000000
=:@0.194299:0.745375:0.204876:0.745375:0.204876:0.729094:0.194299:0.729094:0.000000
+:@0.232040:0.745375:0.242617:0.745375:0.242617:0.729094:0.232040:0.729094:0.000000
ab UaUbU:@0.140222:0.744855:0.266486:0.744855:0.266486:0.728386:0.140222:0.728386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iii):@0.108222:0.764186:0.127275:0.764186:0.127275:0.747472:0.108222:0.747472:0.000000:0.000000:0.000000:0.000000
   (:@0.127284:0.763976:0.149364:0.762718:0.149364:0.746221:0.127284:0.747478:0.000000:0.000000:0.000000:0.000000
):@0.187433:0.762718:0.193385:0.762718:0.193385:0.746221:0.187433:0.746221:0.000000
.:@0.269271:0.762718:0.272026:0.762718:0.272026:0.746221:0.269271:0.746221:0.000000
+:@0.163043:0.763355:0.173619:0.763355:0.173619:0.747074:0.163043:0.747074:0.000000
=:@0.196661:0.763355:0.207237:0.763355:0.207237:0.747074:0.196661:0.747074:0.000000
+:@0.234401:0.763355:0.244978:0.763355:0.244978:0.747074:0.234401:0.747074:0.000000
aU V:@0.134665:0.762834:0.186662:0.762834:0.186662:0.746365:0.134665:0.746365:0.000000:0.000000:0.000000:0.000000
aUaV:@0.211090:0.762834:0.267653:0.762834:0.267653:0.746365:0.211090:0.746365:0.000000:0.000000:0.000000:0.000000
iv):@0.108233:0.781544:0.127036:0.781544:0.127036:0.764829:0.108233:0.764829:0.000000:0.000000:0.000000
  1:@0.127034:0.781326:0.141960:0.781326:0.141960:0.764829:0.127034:0.764829:0.000000:0.000000:0.000000
.  :@0.188794:0.781326:0.199486:0.781326:0.199486:0.764829:0.188794:0.764829:0.000000:0.000000:0.000000
⋅=:@0.141941:0.781963:0.173401:0.781963:0.173401:0.765682:0.141941:0.765682:0.000000:0.000000
VV:@0.147585:0.781442:0.187175:0.781442:0.187175:0.764973:0.147585:0.764973:0.000000:0.000000
Demostración de la propiedad 2:@0.108226:0.815074:0.355280:0.815074:0.355280:0.798128:0.108226:0.798128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.108226:0.839307:0.118764:0.839307:0.118764:0.822592:0.108226:0.822592:0.000000:0.000000
   Por la definición del producto de números reales por pares orde-:@0.118764:0.839091:0.595743:0.839091:0.595743:0.822593:0.118764:0.822593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nados de   y la propiedad distributiva en  , se tiene::@0.131671:0.856441:0.512787:0.856436:0.512787:0.839939:0.131671:0.839944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.200815:0.855473:0.214725:0.855473:0.214725:0.842026:0.200815:0.842026:0.000000
2:@0.214735:0.850083:0.219688:0.850083:0.219688:0.840465:0.214735:0.840465:0.000000
R:@0.434955:0.855468:0.448865:0.855468:0.448865:0.842021:0.434955:0.842021:0.000000
( +  )   = ( +  ) ( ,  ) = (( +  )  ; ( +  )  ).:@0.131970:0.873787:0.475570:0.873787:0.475570:0.857289:0.131970:0.857289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.137927:0.873903:0.146905:0.873903:0.146905:0.857434:0.137927:0.857434:0.000000
 :@0.146905:0.874337:0.151721:0.874337:0.151721:0.855497:0.146905:0.855497:0.000000
b U:@0.166671:0.873903:0.197977:0.873903:0.197977:0.857434:0.166671:0.857434:0.000000:0.000000:0.000000
a:@0.223022:0.873903:0.231999:0.873903:0.231999:0.857434:0.223022:0.857434:0.000000
 :@0.231999:0.874337:0.236816:0.874337:0.236816:0.855497:0.231999:0.855497:0.000000
b p q:@0.251766:0.873903:0.302414:0.873903:0.302414:0.857434:0.251766:0.857434:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.339365:0.873903:0.348342:0.873903:0.348342:0.857434:0.339365:0.857434:0.000000
 :@0.348342:0.874337:0.353159:0.874337:0.353159:0.855497:0.348342:0.855497:0.000000
b p a:@0.368108:0.873903:0.418564:0.873903:0.418564:0.857434:0.368108:0.857434:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.418564:0.874337:0.423380:0.874337:0.423380:0.855497:0.418564:0.855497:0.000000
b q:@0.438330:0.873903:0.466862:0.873903:0.466862:0.857434:0.438330:0.857434:0.000000:0.000000:0.000000
Por otro lado, :@0.131974:0.891138:0.233117:0.891138:0.233117:0.874640:0.131974:0.874640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aU  bU  a p q:@0.233521:0.891254:0.356145:0.891254:0.356145:0.874785:0.233521:0.874785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ :@0.259009:0.891138:0.273959:0.891138:0.273959:0.874640:0.259009:0.874640:0.000000:0.000000
=  ( ,  ) +  ( ,  ) = ( ,  ) + ( ,  ) = :@0.300121:0.891138:0.599869:0.891138:0.599869:0.874640:0.300121:0.874640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b p q:@0.381999:0.891254:0.422976:0.891254:0.422976:0.874785:0.381999:0.874785:0.000000:0.000000:0.000000:0.000000:0.000000
ap aq:@0.454783:0.891254:0.498303:0.891254:0.498303:0.874785:0.454783:0.874785:0.000000:0.000000:0.000000:0.000000:0.000000
bp bq:@0.530110:0.891254:0.574420:0.891254:0.574420:0.874785:0.530110:0.874785:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.131936:0.908489:0.137889:0.908489:0.137889:0.891991:0.131936:0.891991:0.000000
ap:@0.137889:0.908604:0.155979:0.908604:0.155979:0.892136:0.137889:0.892136:0.000000:0.000000
 :@0.155979:0.909038:0.160795:0.909038:0.160795:0.890198:0.155979:0.890198:0.000000
+  , :@0.160795:0.908489:0.201117:0.908489:0.201117:0.891991:0.160795:0.891991:0.000000:0.000000:0.000000:0.000000:0.000000
bp ap:@0.175745:0.908604:0.219207:0.908604:0.219207:0.892136:0.175745:0.892136:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.219207:0.909038:0.224024:0.909038:0.224024:0.890198:0.219207:0.890198:0.000000
+  ) = (( +  )  , ( +  )  ).:@0.224024:0.908489:0.430643:0.908489:0.430643:0.891991:0.224024:0.891991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bq:@0.238973:0.908604:0.257487:0.908604:0.257487:0.892136:0.238973:0.892136:0.000000:0.000000
a:@0.294438:0.908604:0.303416:0.908604:0.303416:0.892136:0.294438:0.892136:0.000000
 :@0.303416:0.909038:0.308232:0.909038:0.308232:0.890198:0.303416:0.890198:0.000000
b p a:@0.323182:0.908604:0.373638:0.908604:0.373638:0.892136:0.323182:0.892136:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.373638:0.909038:0.378454:0.909038:0.378454:0.890198:0.373638:0.890198:0.000000
b q:@0.393404:0.908604:0.421936:0.908604:0.421936:0.892136:0.393404:0.892136:0.000000:0.000000:0.000000
Por la definición de igualdad de elementos de  , se concluye que :@0.131936:0.925839:0.599913:0.925839:0.599913:0.909342:0.131936:0.909342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.457247:0.924871:0.471157:0.924871:0.471157:0.911424:0.457247:0.911424:0.000000
2:@0.471182:0.919487:0.476135:0.919487:0.476135:0.909869:0.471182:0.909869:0.000000
( +  )  = :@0.131980:0.943190:0.212932:0.943190:0.212932:0.926692:0.131980:0.926692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.137933:0.943306:0.146910:0.943306:0.146910:0.926837:0.137933:0.926837:0.000000
 :@0.146910:0.943740:0.151726:0.943740:0.151726:0.924900:0.146910:0.924900:0.000000
b U aU  bU:@0.166676:0.943306:0.274157:0.943306:0.274157:0.926837:0.166676:0.926837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ :@0.237996:0.943190:0.252946:0.943190:0.252946:0.926692:0.237996:0.926692:0.000000:0.000000
= (( +  )  , ( +  )  ).:@0.274157:0.943190:0.437218:0.943190:0.437218:0.926692:0.274157:0.926692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.301013:0.943306:0.309991:0.943306:0.309991:0.926837:0.301013:0.926837:0.000000
 :@0.309991:0.943740:0.314807:0.943740:0.314807:0.924900:0.309991:0.924900:0.000000
b p a:@0.329757:0.943306:0.380212:0.943306:0.380212:0.926837:0.329757:0.926837:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.380212:0.943740:0.385029:0.943740:0.385029:0.924900:0.380212:0.924900:0.000000
b q:@0.399979:0.943306:0.428510:0.943306:0.428510:0.926837:0.399979:0.926837:0.000000:0.000000:0.000000
Conclusión:@0.131691:0.961004:0.218173:0.961004:0.218173:0.944058:0.131691:0.944058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: para todo  ,   :@0.218173:0.960541:0.328985:0.960541:0.328985:0.944043:0.218173:0.944043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.299702:0.960657:0.324843:0.960657:0.324843:0.944188:0.299702:0.944188:0.000000:0.000000:0.000000
 :@0.328985:0.960324:0.349849:0.960324:0.349849:0.945677:0.328985:0.945677:0.000000:0.000000
R:@0.349851:0.959572:0.363761:0.959572:0.363761:0.946125:0.349851:0.946125:0.000000
,   :@0.363761:0.960541:0.386744:0.960541:0.386744:0.944043:0.363761:0.944043:0.000000:0.000000:0.000000:0.000000
U:@0.370658:0.960657:0.382602:0.960657:0.382602:0.944188:0.370658:0.944188:0.000000
 :@0.386744:0.960324:0.407608:0.960324:0.407608:0.945677:0.386744:0.945677:0.000000:0.000000
R:@0.407608:0.959572:0.421518:0.959572:0.421518:0.946125:0.407608:0.946125:0.000000
2:@0.421506:0.954188:0.426459:0.954188:0.426459:0.944570:0.421506:0.944570:0.000000
, ( +  )  = :@0.426458:0.960541:0.513634:0.960541:0.513634:0.944043:0.426458:0.944043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b U  aU  bU:@0.439308:0.960657:0.574859:0.960657:0.574859:0.944188:0.439308:0.944188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ :@0.538698:0.960541:0.553647:0.960541:0.553647:0.944043:0.538698:0.944043:0.000000:0.000000
.:@0.574859:0.960541:0.577613:0.960541:0.577613:0.944043:0.574859:0.944043:0.000000
Competencia :@0.684708:0.093270:0.782331:0.093270:0.782331:0.077797:0.684708:0.077797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684708:0.105838:0.768771:0.105838:0.768771:0.090365:0.684708:0.090365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Antes de describir las :@0.684946:0.130311:0.826544:0.130311:0.826544:0.115248:0.684946:0.115248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades del producto de :@0.638403:0.146153:0.832013:0.146153:0.832013:0.131090:0.638403:0.131090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escalares por elementos de  , :@0.638403:0.161995:0.840286:0.161995:0.840286:0.146932:0.638403:0.146932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.816766:0.161111:0.829466:0.161111:0.829466:0.148833:0.816766:0.148833:0.000000
2:@0.829467:0.156196:0.833990:0.156196:0.833990:0.147414:0.829467:0.147414:0.000000
recordemos algunas propieda-:@0.638405:0.177837:0.835554:0.177837:0.835554:0.162774:0.638405:0.162774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
des del producto “∙” de núme-:@0.638405:0.193679:0.833637:0.193679:0.833637:0.178616:0.638405:0.178616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ros reales.:@0.638405:0.209521:0.700357:0.209521:0.700357:0.194458:0.638405:0.194458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i) Conmutativa:@0.638405:0.232914:0.745230:0.232914:0.745230:0.217442:0.638405:0.217442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: para todo  :@0.745230:0.232492:0.823452:0.232492:0.823452:0.217429:0.745230:0.217429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.638405:0.248440:0.658546:0.248440:0.658546:0.233403:0.638405:0.233403:0.000000:0.000000:0.000000
,   :@0.645230:0.248334:0.662328:0.248334:0.662328:0.233271:0.645230:0.233271:0.000000:0.000000:0.000000:0.000000
 :@0.662328:0.248136:0.681378:0.248136:0.681378:0.234763:0.662328:0.234763:0.000000:0.000000
R:@0.681378:0.247449:0.694078:0.247449:0.694078:0.235172:0.681378:0.235172:0.000000
,   ∙:@0.694078:0.248334:0.717279:0.248334:0.717279:0.233271:0.694078:0.233271:0.000000:0.000000:0.000000:0.000000:0.000000
x y = y  x.:@0.704157:0.248440:0.765915:0.248440:0.765915:0.233403:0.704157:0.233403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.752600:0.248334:0.756382:0.248334:0.756382:0.233271:0.752600:0.233271:0.000000
ii) Asociativa:@0.638405:0.271727:0.729907:0.271727:0.729907:0.256255:0.638405:0.256255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: para todo  :@0.729909:0.271305:0.808130:0.271305:0.808130:0.256242:0.729909:0.256242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y, z:@0.638405:0.287252:0.670857:0.287252:0.670857:0.272216:0.638405:0.272216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, :@0.645230:0.287147:0.651528:0.287147:0.651528:0.272084:0.645230:0.272084:0.000000:0.000000
 :@0.670859:0.287147:0.674641:0.287147:0.674641:0.272084:0.670859:0.272084:0.000000
 :@0.674641:0.286949:0.693691:0.286949:0.693691:0.273575:0.674641:0.273575:0.000000:0.000000
R:@0.693691:0.286262:0.706391:0.286262:0.706391:0.273985:0.693691:0.273985:0.000000
,   ∙ (:@0.706391:0.287147:0.735027:0.287147:0.735027:0.272084:0.706391:0.272084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y ∙ z:@0.716470:0.287252:0.758281:0.287252:0.758281:0.272216:0.716470:0.272216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) = (:@0.758281:0.287147:0.786584:0.287147:0.786584:0.272084:0.758281:0.272084:0.000000:0.000000:0.000000:0.000000:0.000000
x ∙ y z:@0.786584:0.287252:0.832177:0.287252:0.832177:0.272216:0.786584:0.272216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) ∙  .:@0.810594:0.287147:0.834692:0.287147:0.834692:0.272084:0.810594:0.272084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iii) Existencia de elemento :@0.638405:0.310540:0.825333:0.310540:0.825333:0.295068:0.638405:0.295068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
unidad :@0.638405:0.326382:0.694447:0.326382:0.694447:0.310910:0.638405:0.310910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: existe 1:@0.688255:0.325960:0.742290:0.325960:0.742290:0.310897:0.688255:0.310897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.742292:0.325762:0.756944:0.325762:0.756944:0.312388:0.742292:0.312388:0.000000
R:@0.756944:0.325075:0.769644:0.325075:0.769644:0.312798:0.756944:0.312798:0.000000
 tal, que :@0.769644:0.325960:0.824594:0.325960:0.824594:0.310897:0.769644:0.310897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para todo   :@0.638405:0.341802:0.717154:0.341802:0.717154:0.326739:0.638405:0.326739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.706547:0.341907:0.713372:0.341907:0.713372:0.326871:0.706547:0.326871:0.000000
 :@0.717154:0.341604:0.736204:0.341604:0.736204:0.328230:0.717154:0.328230:0.000000:0.000000
R:@0.736207:0.340917:0.748907:0.340917:0.748907:0.328640:0.736207:0.328640:0.000000
, 1 ∙ :@0.748907:0.341802:0.773040:0.341802:0.773040:0.326739:0.748907:0.326739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x = x.:@0.773040:0.341907:0.806901:0.341907:0.806901:0.326871:0.773040:0.326871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iv) Existencia de opuestos :@0.638406:0.365195:0.821568:0.365195:0.821568:0.349723:0.638406:0.349723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplicativos:@0.638406:0.381037:0.744050:0.381037:0.744050:0.365565:0.638406:0.365565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:  :@0.744050:0.380615:0.754129:0.380615:0.754129:0.365551:0.744050:0.365551:0.000000:0.000000:0.000000
para cada   :@0.638406:0.396457:0.715730:0.396457:0.715730:0.381393:0.638406:0.381393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.705123:0.396562:0.711948:0.396562:0.711948:0.381525:0.705123:0.381525:0.000000
 :@0.715730:0.396259:0.734780:0.396259:0.734780:0.382885:0.715730:0.382885:0.000000:0.000000
R:@0.734781:0.395573:0.747481:0.395573:0.747481:0.383296:0.734781:0.383296:0.000000
,  ≠ 0, existe :@0.747481:0.396458:0.832177:0.396458:0.832177:0.381395:0.747481:0.381395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.753778:0.396563:0.764385:0.396563:0.764385:0.381527:0.753778:0.381527:0.000000:0.000000
=∈:@0.666155:0.423940:0.709425:0.423940:0.709425:0.407659:0.666155:0.407659:0.000000:0.000000
−:@0.651024:0.415635:0.657146:0.415635:0.657146:0.406212:0.651024:0.406212:0.000000
x:@0.642125:0.423419:0.649600:0.423419:0.649600:0.406951:0.642125:0.406951:0.000000
x:@0.682907:0.434381:0.690382:0.434381:0.690382:0.417912:0.682907:0.417912:0.000000
1:@0.682750:0.413991:0.691246:0.413991:0.691246:0.397493:0.682750:0.397493:0.000000
1:@0.657045:0.415267:0.661962:0.415267:0.661962:0.405718:0.657045:0.405718:0.000000
, tal que  :@0.725943:0.421726:0.784676:0.421726:0.784676:0.406663:0.725943:0.406663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
xx:@0.784676:0.421831:0.798325:0.421831:0.798325:0.406795:0.784676:0.406795:0.000000:0.000000
–1:@0.798325:0.415925:0.808436:0.415925:0.808436:0.407143:0.798325:0.407143:0.000000:0.000000
 = 1.:@0.808435:0.421726:0.836139:0.421726:0.836139:0.406663:0.808435:0.406663:0.000000:0.000000:0.000000:0.000000:0.000000
La adición y el producto de :@0.638410:0.458110:0.819689:0.458110:0.819689:0.443046:0.638410:0.443046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números reales están ligados :@0.638410:0.473952:0.827165:0.473952:0.827165:0.458888:0.638410:0.458888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por la :@0.638410:0.489794:0.679711:0.489794:0.679711:0.474730:0.638410:0.474730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad distributiva :@0.679711:0.490216:0.843856:0.490216:0.843856:0.474744:0.679711:0.474744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.837664:0.489794:0.840179:0.489794:0.840179:0.474730:0.837664:0.474730:0.000000
para todo  ,  ,   :@0.638410:0.505636:0.742840:0.505636:0.742840:0.490572:0.638410:0.490572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y z:@0.706552:0.505741:0.739058:0.505741:0.739058:0.490704:0.706552:0.490704:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.742840:0.505438:0.761890:0.505438:0.761890:0.492064:0.742840:0.492064:0.000000:0.000000
R:@0.761891:0.504751:0.774591:0.504751:0.774591:0.492473:0.761891:0.492473:0.000000
,  :@0.774591:0.505636:0.784671:0.505636:0.784671:0.490572:0.774591:0.490572:0.000000:0.000000:0.000000
x y + z:@0.638410:0.521583:0.685041:0.521583:0.685041:0.506546:0.638410:0.506546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 (:@0.645234:0.521478:0.654452:0.521478:0.654452:0.506414:0.645234:0.506414:0.000000:0.000000
) = :@0.685041:0.521478:0.707908:0.521478:0.707908:0.506414:0.685041:0.506414:0.000000:0.000000:0.000000:0.000000
xy + xz.:@0.707908:0.521583:0.755295:0.521583:0.755295:0.506546:0.707908:0.506546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El conjunto   en el que se ha :@0.638410:0.544448:0.837139:0.544447:0.837139:0.529384:0.638410:0.529385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.716685:0.543564:0.729385:0.543564:0.729385:0.531286:0.716685:0.531286:0.000000
2:@0.729382:0.538648:0.733904:0.538648:0.733904:0.529866:0.729382:0.529866:0.000000
definido la igualdad, la ope-:@0.638409:0.560289:0.817419:0.560289:0.817419:0.545226:0.638409:0.545226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ración adición \+\ con la que :@0.638409:0.576131:0.828344:0.576131:0.828344:0.561068:0.638409:0.561068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( , +) es grupo conmutativo, :@0.638409:0.591973:0.837052:0.591973:0.837052:0.576910:0.638409:0.576910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.643844:0.591089:0.656544:0.591089:0.656544:0.578811:0.643844:0.578811:0.000000
2:@0.656542:0.586174:0.661065:0.586174:0.661065:0.577392:0.656542:0.577392:0.000000
y el producto de escalares por :@0.638410:0.607815:0.836663:0.607815:0.836663:0.592752:0.638410:0.592752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elemento de   que verifican :@0.638410:0.623657:0.831985:0.623657:0.831985:0.608594:0.638410:0.608594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.723932:0.622773:0.736632:0.622773:0.736632:0.610495:0.723932:0.610495:0.000000
2:@0.736629:0.617858:0.741151:0.617858:0.741151:0.609076:0.736629:0.609076:0.000000
las propiedades del   al   del :@0.638409:0.639499:0.827185:0.639499:0.827185:0.624436:0.638409:0.624436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i:@0.766531:0.639697:0.770418:0.639697:0.770418:0.624436:0.766531:0.624436:0.000000
iv:@0.788571:0.639697:0.800005:0.639697:0.800005:0.624436:0.788571:0.624436:0.000000:0.000000
Teorema precedente, tiene :@0.638409:0.655341:0.815222:0.655341:0.815222:0.640278:0.638409:0.640278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estructura de espacio vectorial.:@0.638409:0.671183:0.838893:0.671183:0.838893:0.656120:0.638409:0.656120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El conjunto   con la adición \+\ :@0.638409:0.694154:0.850157:0.694154:0.850157:0.679091:0.638409:0.679091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.716683:0.693269:0.729383:0.693269:0.729383:0.680992:0.716683:0.680992:0.000000
y el producto \ \ tiene también :@0.638408:0.709996:0.846596:0.709996:0.846596:0.694933:0.638408:0.694933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
×:@0.733937:0.708578:0.743335:0.708578:0.743335:0.694233:0.733937:0.694233:0.000000
estructura de espacio vectorial, :@0.638402:0.725838:0.842671:0.725838:0.842671:0.710775:0.638402:0.710775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pues tiene propiedades simila-:@0.638402:0.741680:0.835655:0.741680:0.835655:0.726617:0.638402:0.726617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
res a las del espacia  .:@0.638402:0.757522:0.785319:0.757522:0.785319:0.742459:0.638402:0.742459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.765579:0.756637:0.778279:0.756637:0.778279:0.744360:0.765579:0.744360:0.000000
2:@0.778280:0.751721:0.782803:0.751721:0.782803:0.742940:0.778280:0.742940:0.000000
 ©:@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