14:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Números reales y funciones:@0.073089:0.043661:0.318030:0.043661:0.318030:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.1 Conjuntos numéricos:@0.293660:0.222619:0.488989:0.222619:0.488989:0.205672:0.293660:0.205672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Hagamos una revisión de los temas tratados sobre los conjuntos numéricos en los :@0.293660:0.257129:0.930910:0.257129:0.930910:0.240695:0.293660:0.240695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 niveles anteriores dada la importancia de los números reales, sus propiedades y :@0.293660:0.273771:0.930960:0.273771:0.930960:0.257337:0.293660:0.257337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 operaciones en el cálculo. :@0.293660:0.290413:0.484757:0.290413:0.484757:0.273979:0.293660:0.273979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Revisemos las operaciones de adición y multiplicación con sus propiedades, tema visto :@0.293660:0.324917:0.931503:0.324917:0.931503:0.308483:0.293660:0.308483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en décimo grado.:@0.293660:0.341559:0.421594:0.341559:0.421594:0.325125:0.293660:0.325125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tema 1. Números reales. Ecuaciones e inecuaciones con o sin :@0.073089:0.083708:0.708505:0.083708:0.708505:0.061840:0.073089:0.061840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 valor absoluto en expresiones racionales:@0.073088:0.103883:0.496067:0.103883:0.496067:0.082014:0.073088:0.082014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Resuelve la siguiente ecuación con valor absoluto: :@0.293660:0.183467:0.661058:0.183467:0.661058:0.167034:0.293660:0.167034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 | 2 |5:@0.660646:0.182913:0.717561:0.182913:0.717561:0.169197:0.660646:0.169197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.665671:0.183467:0.673126:0.183467:0.673126:0.167061:0.665671:0.167061:0.000000 4:@0.688293:0.183467:0.697276:0.183467:0.697276:0.167034:0.688293:0.167034:0.000000 3:@0.717469:0.183467:0.726451:0.183467:0.726451:0.167034:0.717469:0.167034:0.000000 Reto matemático:@0.302768:0.155694:0.437491:0.155694:0.437491:0.138748:0.302768:0.138748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Operaciones y propiedades en números reales :@0.417497:0.399151:0.784614:0.399151:0.784614:0.382204:0.417497:0.382204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.784436:0.398409:0.798330:0.398409:0.798330:0.384926:0.784436:0.384926:0.000000 En el conjunto de los números reales se introducen dos operaciones: adición “ ”, y :@0.301194:0.432941:0.918052:0.432941:0.918052:0.416507:0.301194:0.416507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.571762:0.432081:0.585052:0.432081:0.585052:0.419184:0.571762:0.419184:0.000000 1:@0.880599:0.432386:0.895932:0.432386:0.895932:0.418671:0.880599:0.418671:0.000000 producto “ ”, que se definen a continuación.:@0.301194:0.449583:0.624381:0.449583:0.624381:0.433149:0.301194:0.433149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.380897:0.449028:0.387027:0.449028:0.387027:0.435313:0.380897:0.435313:0.000000 Adición:@0.301194:0.499023:0.359357:0.499023:0.359357:0.482353:0.301194:0.482353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ::@0.359250:0.499023:0.363594:0.499023:0.363594:0.482076:0.359250:0.482076:0.000000 :@0.363521:0.499023:0.367331:0.499023:0.367331:0.482076:0.363521:0.482076:0.000000 es la función denotada “ ” y definida como : :@0.367257:0.499023:0.710994:0.499023:0.710994:0.482589:0.367257:0.482589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.540470:0.498468:0.555803:0.498468:0.555803:0.484753:0.540470:0.484753:0.000000 1:@0.684635:0.498468:0.699968:0.498468:0.699968:0.484753:0.684635:0.484753:0.000000 R:@0.718905:0.487792:0.732799:0.487792:0.732799:0.474309:0.718905:0.474309:0.000000 :@0.732799:0.486920:0.735727:0.486920:0.735727:0.478192:0.732799:0.478192:0.000000 :@0.735610:0.487979:0.750943:0.487979:0.750943:0.474263:0.735610:0.474263:0.000000 :@0.750759:0.486920:0.753688:0.486920:0.753688:0.478192:0.750759:0.478192:0.000000 R:@0.753570:0.487792:0.767465:0.487792:0.767465:0.474309:0.753570:0.474309:0.000000 .:@0.767465:0.488691:0.810474:0.488691:0.810474:0.471510:0.767465:0.471510:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.771678:0.487979:0.789020:0.487979:0.789020:0.471763:0.771678:0.471763:0.000000 R:@0.793231:0.487792:0.807125:0.487792:0.807125:0.474309:0.793231:0.474309:0.000000 (:@0.718911:0.513237:0.724011:0.513237:0.724011:0.496057:0.718911:0.496057:0.000000 x, y:@0.724011:0.513237:0.746565:0.513237:0.746565:0.496086:0.724011:0.496086:0.000000:0.000000:0.000000:0.000000 ) .:@0.746565:0.513237:0.820840:0.513237:0.820840:0.496056:0.746565:0.496057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.755871:0.512524:0.773213:0.512524:0.773213:0.496308:0.755871:0.496308:0.000000 x:@0.777425:0.513237:0.785219:0.513237:0.785219:0.496085:0.777425:0.496085:0.000000 1:@0.789434:0.512657:0.805464:0.512657:0.805464:0.498318:0.789434:0.498318:0.000000 y:@0.809678:0.513237:0.817491:0.513237:0.817491:0.496085:0.809678:0.496085:0.000000 Nota que de la definición de la operación adición se tiene , :@0.301194:0.540682:0.747727:0.540682:0.747727:0.524248:0.301194:0.524248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.721846:0.540682:0.743769:0.540682:0.743769:0.524276:0.721846:0.524276:0.000000:0.000000:0.000000 [ :@0.747665:0.540392:0.766606:0.540392:0.766606:0.526982:0.747665:0.526982:0.000000:0.000000 R :@0.766519:0.539822:0.784319:0.539822:0.784319:0.526925:0.766519:0.526925:0.000000:0.000000 ⇒:@0.784227:0.540127:0.801569:0.540127:0.801569:0.523911:0.784227:0.523911:0.000000 x:@0.801478:0.540682:0.812172:0.540682:0.812172:0.524276:0.801478:0.524276:0.000000:0.000000 :@0.812117:0.540682:0.846704:0.540682:0.846704:0.524248:0.812117:0.524248:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.816075:0.540127:0.831408:0.540127:0.831408:0.526411:0.816075:0.526411:0.000000 y:@0.835273:0.540682:0.842747:0.540682:0.842747:0.524276:0.835273:0.524276:0.000000 [ :@0.846614:0.540392:0.865555:0.540392:0.865555:0.526982:0.846614:0.526982:0.000000:0.000000 R:@0.865466:0.539822:0.878756:0.539822:0.878756:0.526925:0.865466:0.526925:0.000000 . En :@0.878664:0.540682:0.908155:0.540682:0.908155:0.524248:0.878664:0.524248:0.000000:0.000000:0.000000:0.000000:0.000000 este caso, se dice que la suma de números reales es cerrada o conocida como :@0.301192:0.557324:0.868439:0.557324:0.868439:0.540890:0.301192:0.540890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 propiedad clausurativa.:@0.301192:0.573966:0.470182:0.573966:0.470182:0.557532:0.301192:0.557532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Producto: :@0.301192:0.625930:0.378760:0.625930:0.378760:0.609260:0.301192:0.609260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es la función denotada “ ” y definida como : :@0.378668:0.625930:0.719810:0.625930:0.719810:0.609496:0.378668:0.609496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.555820:0.625375:0.561949:0.625375:0.561949:0.611659:0.555820:0.611659:0.000000 ?:@0.694739:0.625375:0.700869:0.625375:0.700869:0.611659:0.694739:0.611659:0.000000 R:@0.727703:0.612175:0.741597:0.612175:0.741597:0.598691:0.727703:0.598691:0.000000 :@0.741597:0.611302:0.744526:0.611302:0.744526:0.602574:0.741597:0.602574:0.000000 :@0.744409:0.612362:0.759742:0.612362:0.759742:0.598646:0.744409:0.598646:0.000000 :@0.759558:0.611302:0.762486:0.611302:0.762486:0.602574:0.759558:0.602574:0.000000 R:@0.762369:0.612175:0.776263:0.612175:0.776263:0.598691:0.762369:0.598691:0.000000 .:@0.776263:0.613074:0.819273:0.613074:0.819273:0.595893:0.776263:0.595893:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.780477:0.612362:0.797819:0.612362:0.797819:0.596145:0.780477:0.596145:0.000000 R:@0.802030:0.612175:0.815924:0.612175:0.815924:0.598691:0.802030:0.598691:0.000000 (:@0.727710:0.637620:0.732810:0.637620:0.732810:0.620439:0.727710:0.620439:0.000000 x, y:@0.732810:0.637620:0.755363:0.637620:0.755363:0.620468:0.732810:0.620468:0.000000:0.000000:0.000000:0.000000 ) :@0.755363:0.637620:0.786224:0.637619:0.786224:0.620438:0.755363:0.620439:0.000000:0.000000:0.000000:0.000000 →:@0.764672:0.636907:0.782014:0.636907:0.782014:0.620691:0.764672:0.620691:0.000000 x y:@0.786224:0.637619:0.815167:0.637619:0.815167:0.620467:0.786224:0.620467:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.797482:0.637039:0.803890:0.637039:0.803890:0.622700:0.797482:0.622700:0.000000 .:@0.815167:0.637619:0.818515:0.637619:0.818515:0.620438:0.815167:0.620438:0.000000 De la definición de la operación producto tenemos , :@0.301194:0.667593:0.666118:0.667593:0.666118:0.651160:0.301194:0.651160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.642814:0.667593:0.662804:0.667593:0.662804:0.651187:0.642814:0.651187:0.000000:0.000000:0.000000 [ :@0.665411:0.667304:0.683737:0.667304:0.683737:0.653894:0.665411:0.653894:0.000000:0.000000 R :@0.683035:0.666734:0.700191:0.666734:0.700191:0.653836:0.683035:0.653836:0.000000:0.000000 ⇒ :@0.699455:0.667039:0.720487:0.667039:0.720487:0.650822:0.699455:0.650822:0.000000:0.000000 x y:@0.719780:0.667593:0.746010:0.667593:0.746010:0.651187:0.719780:0.651187:0.000000:0.000000:0.000000 :@0.726517:0.667593:0.749323:0.667593:0.749323:0.651160:0.726517:0.651160:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.729830:0.667039:0.735960:0.667039:0.735960:0.653323:0.729830:0.653323:0.000000 [ :@0.748599:0.667304:0.766925:0.667304:0.766925:0.653894:0.748599:0.653894:0.000000:0.000000 R:@0.766223:0.666734:0.779513:0.666734:0.779513:0.653836:0.766223:0.653836:0.000000 . Entonces, se dice :@0.778777:0.667593:0.913588:0.667593:0.913588:0.651160:0.778777:0.651160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que la multiplicación de números reales es cerrada.:@0.301200:0.684235:0.671661:0.684235:0.671661:0.667802:0.301200:0.667802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Propiedades:@0.450098:0.741253:0.549087:0.741253:0.549087:0.724306:0.450098:0.724306:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Adición:@0.083002:0.775049:0.143321:0.775049:0.143321:0.758102:0.083002:0.758102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Conmutativa::@0.082994:0.802407:0.215414:0.802407:0.215414:0.785738:0.082994:0.785738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para todo:@0.215298:0.802407:0.290171:0.802407:0.290171:0.785974:0.215298:0.785974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x, y :@0.290031:0.802407:0.317863:0.802407:0.317863:0.786001:0.290031:0.786001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [ :@0.317841:0.802117:0.336782:0.802117:0.336782:0.788708:0.317841:0.788708:0.000000:0.000000 R:@0.336694:0.801429:0.349380:0.801429:0.349380:0.789118:0.336694:0.789118:0.000000 , x y y x.:@0.349292:0.802407:0.457158:0.802407:0.457158:0.786001:0.349292:0.786001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5 1:@0.369687:0.801853:0.443298:0.801853:0.443298:0.788137:0.369687:0.788137:0.000000:0.000000:0.000000:0.000000:0.000000 2. Asociativa::@0.082994:0.829771:0.194209:0.829771:0.194209:0.813101:0.082994:0.813101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para todo:@0.194093:0.829771:0.268966:0.829771:0.268966:0.813337:0.194093:0.813337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x, y, z :@0.268826:0.829771:0.309661:0.829771:0.309661:0.813365:0.268826:0.813365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [ :@0.309656:0.829481:0.328597:0.829481:0.328597:0.816071:0.309656:0.816071:0.000000:0.000000 R:@0.328509:0.828792:0.341195:0.828792:0.341195:0.816481:0.328509:0.816481:0.000000 ,:@0.341107:0.829771:0.344310:0.829771:0.344310:0.813337:0.341107:0.813337:0.000000 x y z x y z.:@0.344237:0.829771:0.525861:0.829771:0.525861:0.813365:0.344237:0.813365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.361374:0.829216:0.376707:0.829216:0.376707:0.815500:0.361374:0.815500:0.000000 (:@0.379855:0.829771:0.384733:0.829771:0.384733:0.813337:0.379855:0.813337:0.000000 1 5:@0.395317:0.829216:0.444354:0.829216:0.444354:0.815500:0.395317:0.815500:0.000000:0.000000:0.000000 ):@0.420976:0.829771:0.425854:0.829771:0.425854:0.813337:0.420976:0.813337:0.000000 (:@0.447501:0.829771:0.452379:0.829771:0.452379:0.813337:0.447501:0.813337:0.000000 1:@0.462945:0.829216:0.478278:0.829216:0.478278:0.815500:0.462945:0.815500:0.000000 ):@0.488844:0.829771:0.493722:0.829771:0.493722:0.813337:0.488844:0.813337:0.000000 1:@0.496888:0.829216:0.512221:0.829216:0.512221:0.815500:0.496888:0.815500:0.000000 3. Existencia de elemento neutro::@0.082994:0.857133:0.331928:0.857133:0.331928:0.840463:0.082994:0.840463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 existe 0:@0.331190:0.857133:0.385263:0.857133:0.385263:0.840699:0.331190:0.840699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.384589:0.857133:0.387903:0.857133:0.387903:0.840727:0.384589:0.840727:0.000000 [ :@0.387273:0.856843:0.406214:0.856843:0.406214:0.843433:0.387273:0.843433:0.000000:0.000000 R:@0.406126:0.856154:0.418812:0.856154:0.418812:0.843843:0.406126:0.843843:0.000000 ,tal que para todo:@0.418724:0.857133:0.540720:0.857133:0.540720:0.840699:0.418724:0.840699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.421853:0.857133:0.425167:0.857133:0.425167:0.840727:0.421853:0.840727:0.000000 x :@0.539991:0.857133:0.552821:0.857133:0.552821:0.840727:0.539991:0.840727:0.000000:0.000000:0.000000 [ :@0.552210:0.856843:0.571151:0.856843:0.571151:0.843433:0.552210:0.843433:0.000000:0.000000 R:@0.571063:0.856154:0.583749:0.856154:0.583749:0.843843:0.571063:0.843843:0.000000 ,:@0.583661:0.857133:0.586864:0.857133:0.586864:0.840699:0.583661:0.840699:0.000000 x x x.:@0.586330:0.857133:0.723041:0.857133:0.723041:0.840727:0.586330:0.840727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5 1 5:@0.603468:0.856578:0.709180:0.856578:0.709180:0.842862:0.603468:0.842862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.621948:0.857133:0.630931:0.857133:0.630931:0.840699:0.621948:0.840699:0.000000 0:@0.652578:0.857133:0.661561:0.857133:0.661561:0.840699:0.652578:0.840699:0.000000 4. Existencia de opuestos aditivos::@0.082994:0.884496:0.352679:0.884496:0.352679:0.867826:0.082994:0.867826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.352469:0.884496:0.356279:0.884496:0.356279:0.867549:0.352469:0.867549:0.000000 para cada:@0.356205:0.884496:0.426889:0.884496:0.426889:0.868062:0.356205:0.868062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.426760:0.884496:0.440695:0.884496:0.440695:0.868090:0.426760:0.868090:0.000000:0.000000:0.000000 [ :@0.440639:0.884206:0.459580:0.884206:0.459580:0.870796:0.440639:0.870796:0.000000:0.000000 R:@0.459492:0.883517:0.472178:0.883517:0.472178:0.871206:0.459492:0.871206:0.000000 , existe:@0.472090:0.884496:0.520126:0.884496:0.520126:0.868062:0.472090:0.868062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.475219:0.884496:0.478533:0.884496:0.478533:0.868090:0.475219:0.868090:0.000000 x :@0.520022:0.884496:0.549198:0.884496:0.549198:0.868090:0.520022:0.868090:0.000000:0.000000:0.000000:0.000000 2:@0.523262:0.883941:0.538595:0.883941:0.538595:0.870225:0.523262:0.870225:0.000000 [ :@0.549143:0.884206:0.568084:0.884206:0.568084:0.870796:0.549143:0.870796:0.000000:0.000000 R:@0.567996:0.883517:0.580682:0.883517:0.580682:0.871206:0.567996:0.871206:0.000000 , tal que x:@0.580594:0.884496:0.652217:0.884496:0.652217:0.868062:0.580594:0.868062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.583723:0.884496:0.590276:0.884496:0.590276:0.868090:0.583723:0.868090:0.000000:0.000000 :@0.652088:0.884496:0.673882:0.884496:0.673882:0.868090:0.652088:0.868090:0.000000:0.000000:0.000000 1 2 5 2 1 5:@0.655328:0.883941:0.798094:0.883941:0.798094:0.870225:0.655328:0.870225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.673808:0.884496:0.678686:0.884496:0.678686:0.868062:0.673808:0.868062:0.000000 x x x .:@0.693854:0.884496:0.813483:0.884496:0.813483:0.868090:0.693854:0.868090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.701235:0.884496:0.706113:0.884496:0.706113:0.868062:0.701235:0.868062:0.000000 0:@0.801242:0.884496:0.810225:0.884496:0.810225:0.868062:0.801242:0.868062:0.000000 Las propiedades de la 1 a la 4 dan la :@0.082991:0.911858:0.349419:0.911858:0.349419:0.895424:0.082991:0.895424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estructura:@0.349399:0.911858:0.427013:0.911858:0.427013:0.895188:0.349399:0.895188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 algebraica que denominamos grupo conmutativo de la adición de :@0.426912:0.911858:0.920598:0.911858:0.920598:0.895424:0.426912:0.895424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números reales, que se escribe ( , ).:@0.083009:0.928500:0.356688:0.928500:0.356688:0.912066:0.083009:0.912066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.313173:0.927640:0.326464:0.927640:0.326464:0.914742:0.313173:0.914742:0.000000 1:@0.333440:0.927945:0.348773:0.927945:0.348773:0.914229:0.333440:0.914229:0.000000 t.ly/40pxH:@0.104396:0.518236:0.178551:0.518236:0.178551:0.501802:0.104396:0.501802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Qué son los :@0.080269:0.386779:0.175341:0.386779:0.175341:0.369832:0.080269:0.369832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números reales:@0.080269:0.403421:0.200814:0.403421:0.200814:0.386474:0.080269:0.386474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.1. Describe propiedades de los números y las operaciones que son comunes y diferentes en los distintos sistemas numéricos.:@0.249101:0.969553:0.915714:0.969553:0.915714:0.957602:0.249101:0.957602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y x :@0.754961:0.182668:0.804978:0.182668:0.804978:0.172228:0.754961:0.172228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.761813:0.182315:0.771571:0.182315:0.771571:0.173587:0.761813:0.173587:0.000000 7:@0.773679:0.182668:0.779396:0.182668:0.779396:0.172210:0.773679:0.172210:0.000000 5:@0.793113:0.182315:0.802870:0.182315:0.802870:0.173587:0.793113:0.173587:0.000000 1:@0.804978:0.182668:0.810695:0.182668:0.810695:0.172210:0.804978:0.172210:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000