24:@0.037229:0.974518:0.056728:0.974518:0.056728:0.957377:0.037229:0.957377:0.000000:0.000000 Estructura algebraica y orden en los números reales:@0.073089:0.043661:0.532427:0.043661:0.532427:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De acuerdo con las definiciones sobre las relaciones de orden “menor que” y ”mayor que”, :@0.293660:0.241789:0.930893:0.241789:0.930893:0.226077:0.293660:0.226077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 establecidas en los conjuntos de los números naturales, enteros, racionales, podemos :@0.293660:0.258431:0.930879:0.258431:0.930879:0.242719:0.293660:0.242719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 definir estas relaciones en el conjunto de los números reales como se indica a :@0.293660:0.275073:0.930938:0.275073:0.930938:0.259360:0.293660:0.259360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.773850:0.274213:0.787140:0.274213:0.787140:0.261316:0.773850:0.261316:0.000000 continuación.:@0.293660:0.291715:0.393096:0.291715:0.393096:0.276002:0.293660:0.276002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.293660:0.316220:0.371628:0.316220:0.371628:0.299550:0.293660:0.299550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean , :@0.371523:0.316220:0.443882:0.316220:0.443882:0.300507:0.371523:0.300507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.418001:0.316220:0.439924:0.316220:0.439924:0.300785:0.418001:0.300785:0.000000:0.000000:0.000000 .:@0.475947:0.316219:0.479150:0.316219:0.479150:0.300506:0.475947:0.300506:0.000000 i. Diremos que “ es menor que ”, que se escribe “ ”, si solo si :@0.293660:0.340723:0.827773:0.340723:0.827773:0.325010:0.293660:0.325010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.418488:0.340723:0.425943:0.340723:0.425943:0.325287:0.418488:0.325287:0.000000 y:@0.534435:0.340723:0.541909:0.340723:0.541909:0.325287:0.534435:0.325287:0.000000 x:@0.663452:0.340723:0.670907:0.340723:0.670907:0.325287:0.663452:0.325287:0.000000 ,:@0.674791:0.340168:0.690124:0.340168:0.690124:0.326452:0.674791:0.326452:0.000000 y:@0.693989:0.340723:0.701463:0.340723:0.701463:0.325287:0.693989:0.325287:0.000000 y:@0.725963:0.340723:0.733436:0.340723:0.733436:0.325287:0.725963:0.325287:0.000000 y:@0.785805:0.340723:0.793278:0.340723:0.793278:0.325287:0.785805:0.325287:0.000000 2:@0.797162:0.340168:0.812495:0.340168:0.812495:0.326452:0.797162:0.326452:0.000000 x:@0.816361:0.340723:0.823816:0.340723:0.823816:0.325287:0.816361:0.325287:0.000000 +:@0.859817:0.334659:0.866213:0.334659:0.866213:0.325498:0.859817:0.325498:0.000000 .:@0.866166:0.340723:0.869369:0.340723:0.869369:0.325010:0.866166:0.325010:0.000000 ii. Diremos que “ es mayor que ”, que se escribe “ :@0.293660:0.357364:0.771606:0.357364:0.771606:0.341652:0.293660:0.341652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.441693:0.357364:0.449148:0.357364:0.449148:0.341929:0.441693:0.341929:0.000000 y:@0.590184:0.357364:0.597658:0.357364:0.597658:0.341929:0.590184:0.341929:0.000000 x:@0.759365:0.357364:0.766820:0.357364:0.766820:0.341929:0.759365:0.341929:0.000000 .:@0.777570:0.356810:0.792903:0.356810:0.792903:0.343094:0.777570:0.343094:0.000000 ”, si solo si :@0.793971:0.357364:0.930884:0.357364:0.930884:0.341652:0.793971:0.341652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.803966:0.357364:0.811439:0.357364:0.811439:0.341929:0.803966:0.341929:0.000000 y:@0.852911:0.357364:0.860384:0.357364:0.860384:0.341929:0.852911:0.341929:0.000000 y:@0.317315:0.374006:0.324788:0.374006:0.324788:0.358571:0.317315:0.358571:0.000000 ; o sea, :@0.324715:0.374006:0.448945:0.374006:0.448945:0.358294:0.324715:0.358294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.328672:0.373452:0.344006:0.373452:0.344006:0.359736:0.328672:0.359736:0.000000 x:@0.347871:0.374006:0.355326:0.374006:0.355326:0.358571:0.347871:0.358571:0.000000 x:@0.406977:0.374006:0.414432:0.374006:0.414432:0.358571:0.406977:0.358571:0.000000 2:@0.418316:0.373452:0.433649:0.373452:0.433649:0.359736:0.418316:0.359736:0.000000 y:@0.437514:0.374006:0.444988:0.374006:0.444988:0.358571:0.437514:0.358571:0.000000 +:@0.481049:0.367942:0.487445:0.367942:0.487445:0.358782:0.481049:0.358782:0.000000 .:@0.487398:0.374006:0.490601:0.374006:0.490601:0.358294:0.487398:0.358294:0.000000 Ejercicio resuelto:@0.293662:0.397790:0.422244:0.397790:0.422244:0.381121:0.293662:0.381121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si :@0.293662:0.421574:0.328212:0.421574:0.328212:0.405862:0.293662:0.405862:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.316137:0.421574:0.323592:0.421574:0.323592:0.406139:0.316137:0.406139:0.000000 5:@0.332851:0.421019:0.348184:0.421019:0.348184:0.407304:0.332851:0.407304:0.000000 1 :@0.348994:0.421574:0.371386:0.421574:0.371386:0.405862:0.348994:0.405862:0.000000:0.000000:0.000000:0.000000 1:@0.376043:0.421019:0.391377:0.421019:0.391377:0.407304:0.376043:0.407304:0.000000 2 , :@0.392177:0.421574:0.449466:0.421586:0.449466:0.405873:0.392177:0.405862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.437372:0.421586:0.444846:0.421586:0.444846:0.406150:0.437372:0.406150:0.000000 5:@0.454104:0.421031:0.469438:0.421031:0.469438:0.407315:0.454104:0.407315:0.000000 3 :@0.470248:0.421586:0.506876:0.421586:0.506876:0.405873:0.470248:0.405873:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.511515:0.421031:0.526848:0.421031:0.526848:0.407315:0.511515:0.407315:0.000000 1, entonces :@0.527658:0.421586:0.653048:0.421586:0.653048:0.405873:0.527658:0.405873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.640973:0.421586:0.648428:0.421586:0.648428:0.406150:0.640973:0.406150:0.000000 .:@0.657687:0.421031:0.673020:0.421031:0.673020:0.407315:0.657687:0.407315:0.000000 0, :@0.673830:0.421586:0.716866:0.421586:0.716866:0.405873:0.673830:0.405873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.704782:0.421586:0.712255:0.421586:0.712255:0.406150:0.704782:0.406150:0.000000 .:@0.721505:0.421031:0.736838:0.421031:0.736838:0.407315:0.721505:0.407315:0.000000 0 y, en consecuencia, :@0.737648:0.421586:0.930924:0.421586:0.930924:0.405873:0.737648:0.405873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.293647:0.438227:0.301102:0.438227:0.301102:0.422792:0.293647:0.422792:0.000000 1 2 3 1 2 3 0. :@0.301028:0.438227:0.620096:0.438227:0.620096:0.422515:0.301028:0.422515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5 1:@0.304986:0.437673:0.382922:0.437673:0.382922:0.423957:0.304986:0.423957:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.324184:0.438227:0.331658:0.438227:0.331658:0.422792:0.324184:0.422792:0.000000 1:@0.413876:0.437673:0.429209:0.437673:0.429209:0.423957:0.413876:0.423957:0.000000 2 5:@0.460155:0.437673:0.507536:0.437673:0.507536:0.423957:0.460155:0.423957:0.000000:0.000000:0.000000 1:@0.538477:0.437673:0.553810:0.437673:0.553810:0.423957:0.538477:0.423957:0.000000 .:@0.584754:0.437673:0.600087:0.437673:0.600087:0.423957:0.584754:0.423957:0.000000 Asimismo, (1 2) ( 3 1) 0.:@0.293662:0.462011:0.578645:0.462016:0.578645:0.446304:0.293662:0.446299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xy:@0.371745:0.462011:0.386803:0.462011:0.386803:0.446576:0.371745:0.446576:0.000000:0.000000 5:@0.390705:0.461457:0.406038:0.461457:0.406038:0.447741:0.390705:0.447741:0.000000 1:@0.427538:0.461457:0.442871:0.461457:0.442871:0.447741:0.427538:0.447741:0.000000 2:@0.510501:0.461462:0.525834:0.461462:0.525834:0.447746:0.510501:0.447746:0.000000 .:@0.547334:0.461462:0.562667:0.461462:0.562667:0.447746:0.547334:0.447746:0.000000 Teorema. Sean , , :@0.293663:0.485800:0.442652:0.485800:0.442652:0.470088:0.293663:0.470088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.399284:0.485800:0.438694:0.485800:0.438694:0.470365:0.399284:0.470365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.474717:0.485807:0.477920:0.485807:0.477920:0.470094:0.474717:0.470094:0.000000 i. Si , entonces .:@0.293660:0.509596:0.532471:0.509596:0.532471:0.493883:0.293660:0.493883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.333554:0.509596:0.341009:0.509596:0.341009:0.494160:0.333554:0.494160:0.000000 ,:@0.344893:0.509041:0.360226:0.509041:0.360226:0.495325:0.344893:0.495325:0.000000 y y:@0.364091:0.509596:0.386033:0.509596:0.386033:0.494160:0.364091:0.494160:0.000000:0.000000:0.000000 ,:@0.389917:0.509041:0.405250:0.509041:0.405250:0.495325:0.389917:0.495325:0.000000 z:@0.409115:0.509596:0.416349:0.509596:0.416349:0.494160:0.409115:0.494160:0.000000 x:@0.491562:0.509596:0.499016:0.509596:0.499016:0.494160:0.491562:0.494160:0.000000 ,:@0.502900:0.509041:0.518234:0.509041:0.518234:0.495325:0.502900:0.495325:0.000000 z:@0.522099:0.509596:0.529333:0.509596:0.529333:0.494160:0.522099:0.494160:0.000000 ii.:@0.603247:0.509596:0.613997:0.509596:0.613997:0.493883:0.603247:0.493883:0.000000:0.000000:0.000000 x:@0.628337:0.509596:0.635792:0.509596:0.635792:0.494160:0.628337:0.494160:0.000000 , si y solo si .:@0.635719:0.509596:0.850071:0.509596:0.850071:0.493883:0.635719:0.493883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.639676:0.509041:0.655010:0.509041:0.655010:0.495325:0.639676:0.495325:0.000000 y:@0.658875:0.509596:0.666348:0.509596:0.666348:0.494160:0.658875:0.494160:0.000000 x:@0.748298:0.509596:0.755752:0.509596:0.755752:0.494160:0.748298:0.494160:0.000000 1 , 1:@0.759636:0.509041:0.835842:0.509041:0.835842:0.495325:0.759636:0.495325:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.778835:0.509596:0.786069:0.509596:0.786069:0.494160:0.778835:0.494160:0.000000 y:@0.809152:0.509596:0.816625:0.509596:0.816625:0.494160:0.809152:0.494160:0.000000 z:@0.839708:0.509596:0.846942:0.509596:0.846942:0.494160:0.839708:0.494160:0.000000 Ejercicio resuelto:@0.293675:0.535169:0.422257:0.535169:0.422257:0.518499:0.293675:0.518499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea :@0.293675:0.560742:0.334705:0.560742:0.334705:0.545029:0.293675:0.545029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.323292:0.560742:0.330747:0.560742:0.330747:0.545306:0.323292:0.545306:0.000000 . Se tiene 1 y 1 2, entonces, 2.:@0.366755:0.560748:0.778410:0.560748:0.778410:0.545035:0.366755:0.545035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.435980:0.560748:0.443435:0.560748:0.443435:0.545313:0.435980:0.545313:0.000000 , 1:@0.447319:0.560193:0.493190:0.560193:0.493190:0.546477:0.447319:0.546477:0.000000:0.000000:0.000000 x:@0.466518:0.560748:0.473973:0.560748:0.473973:0.545313:0.466518:0.545313:0.000000 x:@0.521868:0.560748:0.529323:0.560748:0.529323:0.545313:0.521868:0.545313:0.000000 1 , 1:@0.533207:0.560193:0.611125:0.560193:0.611125:0.546477:0.533207:0.546477:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.584453:0.560748:0.591908:0.560748:0.591908:0.545313:0.584453:0.545313:0.000000 x:@0.705223:0.560748:0.712678:0.560748:0.712678:0.545313:0.705223:0.545313:0.000000 , 1:@0.716562:0.560193:0.762433:0.560193:0.762433:0.546477:0.716562:0.546477:0.000000:0.000000:0.000000 x:@0.735761:0.560748:0.743215:0.560748:0.743215:0.545313:0.735761:0.545313:0.000000 Teorema:@0.293692:0.586321:0.359693:0.586321:0.359693:0.569651:0.293692:0.569651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean :@0.359590:0.586321:0.406190:0.586321:0.406190:0.570608:0.359590:0.570608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a, b, c:@0.406068:0.586321:0.444731:0.586321:0.444731:0.570886:0.406068:0.570886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.444705:0.586321:0.448736:0.586321:0.448736:0.570608:0.444705:0.570608:0.000000 . Se verifican las siguientes propiedades::@0.480761:0.586325:0.769389:0.586325:0.769389:0.570612:0.480761:0.570612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i. Si y 0, entonces .:@0.293660:0.611900:0.568982:0.611900:0.568982:0.596187:0.293660:0.596187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.333554:0.611900:0.342813:0.611900:0.342813:0.596465:0.333554:0.596465:0.000000 ,:@0.346696:0.611345:0.362030:0.611345:0.362030:0.597630:0.346696:0.597630:0.000000 b c:@0.365895:0.611900:0.398660:0.611900:0.398660:0.596465:0.365895:0.596465:0.000000:0.000000:0.000000 .:@0.402544:0.611345:0.417877:0.611345:0.417877:0.597630:0.402544:0.597630:0.000000 ac:@0.509048:0.611900:0.525891:0.611900:0.525891:0.596465:0.509048:0.596465:0.000000:0.000000 ,:@0.529793:0.611345:0.545127:0.611345:0.545127:0.597630:0.529793:0.597630:0.000000 bc:@0.548992:0.611900:0.565835:0.611900:0.565835:0.596465:0.548992:0.596465:0.000000:0.000000 ii. Si y 0, entonces :@0.293660:0.628542:0.529867:0.628542:0.529867:0.612829:0.293660:0.612829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.333554:0.628542:0.342813:0.628542:0.342813:0.613107:0.333554:0.613107:0.000000 ,:@0.346696:0.627987:0.362030:0.627987:0.362030:0.614272:0.346696:0.614272:0.000000 b c:@0.365895:0.628542:0.398660:0.628542:0.398660:0.613107:0.365895:0.613107:0.000000:0.000000:0.000000 ,:@0.402544:0.627987:0.417877:0.627987:0.417877:0.614272:0.402544:0.614272:0.000000 ac:@0.509048:0.628542:0.525891:0.628542:0.525891:0.613107:0.509048:0.613107:0.000000:0.000000 .:@0.529793:0.627987:0.545127:0.627987:0.545127:0.614272:0.529793:0.614272:0.000000 bc:@0.545035:0.628542:0.565117:0.628542:0.565117:0.613107:0.545035:0.613107:0.000000:0.000000:0.000000 .:@0.565062:0.628542:0.568265:0.628542:0.568265:0.612829:0.565062:0.612829:0.000000 iii. Si 0 y 0, entonces 0.:@0.293660:0.645184:0.564012:0.645184:0.564012:0.629471:0.293660:0.629471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.333554:0.645184:0.342813:0.645184:0.342813:0.629748:0.333554:0.629748:0.000000 ,:@0.346696:0.644629:0.362030:0.644629:0.362030:0.630913:0.346696:0.630913:0.000000 b:@0.390708:0.645184:0.399967:0.645184:0.399967:0.629748:0.390708:0.629748:0.000000 .:@0.403851:0.644629:0.419184:0.644629:0.419184:0.630913:0.403851:0.630913:0.000000 ab:@0.510355:0.645184:0.528799:0.645184:0.528799:0.629748:0.510355:0.629748:0.000000:0.000000 ,:@0.532702:0.644629:0.548035:0.644629:0.548035:0.630913:0.532702:0.630913:0.000000 iv. Si 0 y 0, entonces 0.:@0.293660:0.661826:0.564012:0.661826:0.564012:0.646113:0.293660:0.646113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.333554:0.661826:0.342813:0.661826:0.342813:0.646390:0.333554:0.646390:0.000000 ,:@0.346696:0.661271:0.362030:0.661271:0.362030:0.647555:0.346696:0.647555:0.000000 b:@0.390708:0.661826:0.399967:0.661826:0.399967:0.646390:0.390708:0.646390:0.000000 ,:@0.403851:0.661271:0.419184:0.661271:0.419184:0.647555:0.403851:0.647555:0.000000 ab:@0.510355:0.661826:0.528799:0.661826:0.528799:0.646390:0.510355:0.646390:0.000000:0.000000 .:@0.532702:0.661271:0.548035:0.661271:0.548035:0.647555:0.532702:0.647555:0.000000 v. Si 0, entonces 0.:@0.293660:0.678467:0.502852:0.678467:0.502852:0.662755:0.293660:0.662755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.333554:0.678467:0.342813:0.678467:0.342813:0.663032:0.333554:0.663032:0.000000 Þ:@0.346696:0.677913:0.362030:0.677913:0.362030:0.664197:0.346696:0.664197:0.000000 a:@0.453201:0.678467:0.462460:0.678467:0.462460:0.663032:0.453201:0.663032:0.000000 2:@0.462393:0.672403:0.467630:0.672403:0.467630:0.663243:0.462393:0.663243:0.000000 .:@0.471541:0.677913:0.486874:0.677913:0.486874:0.664197:0.471541:0.664197:0.000000 Ejercicio resuelto:@0.293672:0.704040:0.422254:0.704040:0.422254:0.687371:0.293672:0.687371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea :@0.293672:0.729613:0.323392:0.729613:0.323392:0.713901:0.293672:0.713901:0.000000:0.000000:0.000000:0.000000 x :@0.323547:0.729613:0.334241:0.729613:0.334241:0.714178:0.323547:0.714178:0.000000:0.000000 . Se tiene, 3 , y como 2 0, entonces, 2 ( 3) 2 , de donde :@0.366514:0.729621:0.930929:0.729621:0.930929:0.713908:0.366514:0.713908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.439439:0.729621:0.446894:0.729621:0.446894:0.714186:0.439439:0.714186:0.000000 2 ,:@0.451017:0.729066:0.498894:0.729066:0.498894:0.715351:0.451017:0.715351:0.000000:0.000000:0.000000 x:@0.502999:0.729621:0.510454:0.729621:0.510454:0.714186:0.502999:0.714186:0.000000 2 ,:@0.576683:0.729066:0.620364:0.729066:0.620364:0.715351:0.576683:0.715351:0.000000:0.000000:0.000000 2:@0.715216:0.729066:0.730550:0.729066:0.730550:0.715351:0.715216:0.715351:0.000000 x:@0.748368:0.729621:0.755823:0.729621:0.755823:0.714186:0.748368:0.714186:0.000000 2:@0.759946:0.729066:0.775279:0.729066:0.775279:0.715351:0.759946:0.715351:0.000000 . 2:@0.797294:0.729066:0.832066:0.729066:0.832066:0.715351:0.797294:0.715351:0.000000:0.000000:0.000000 x:@0.840883:0.729621:0.848338:0.729621:0.848338:0.714186:0.840883:0.714186:0.000000 6 2 2 .:@0.293617:0.746263:0.399826:0.746263:0.399826:0.730550:0.293617:0.730550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.306465:0.745708:0.321798:0.745708:0.321798:0.731992:0.306465:0.731992:0.000000 x:@0.334554:0.746263:0.342009:0.746263:0.342009:0.730827:0.334554:0.730827:0.000000 . 2:@0.345893:0.745708:0.380425:0.745708:0.380425:0.731992:0.345893:0.731992:0.000000:0.000000:0.000000 x:@0.389242:0.746263:0.396697:0.746263:0.396697:0.730827:0.389242:0.730827:0.000000 2.1. Intervalos:@0.293617:0.771836:0.404397:0.771836:0.404397:0.754889:0.293617:0.754889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Los intervalos son conjuntos (:@0.293617:0.799198:0.516322:0.799198:0.516322:0.783485:0.293617:0.783485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 subconjuntos:@0.516547:0.799198:0.621871:0.799198:0.621871:0.782528:0.516547:0.782528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de ), por lo tanto, podemos realizar las :@0.622002:0.799198:0.930706:0.799198:0.930706:0.783485:0.622002:0.783485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.650947:0.798338:0.664237:0.798338:0.664237:0.785440:0.650947:0.785440:0.000000 operaciones de unión, intersección, diferencia, complemento y diferencia simétrica.:@0.293617:0.815839:0.897529:0.815839:0.897529:0.800127:0.293617:0.800127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Intervalos acotados:@0.293617:0.839623:0.441824:0.839623:0.441824:0.822954:0.293617:0.822954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición.:@0.293617:0.863407:0.375321:0.863407:0.375321:0.846738:0.293617:0.846738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , :@0.375198:0.863407:0.448035:0.863407:0.448035:0.847695:0.375198:0.847695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.418565:0.863407:0.444078:0.863407:0.444078:0.847972:0.418565:0.847972:0.000000:0.000000:0.000000 con .:@0.480146:0.863422:0.560403:0.863422:0.560403:0.847710:0.480146:0.847710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.515673:0.863422:0.524932:0.863422:0.524932:0.847987:0.515673:0.847987:0.000000 ,:@0.528816:0.862868:0.544149:0.862868:0.544149:0.849152:0.528816:0.849152:0.000000 b:@0.548015:0.863422:0.557274:0.863422:0.557274:0.847987:0.548015:0.847987:0.000000 i. Se llama intervalo cerrado de extremos y al subconjunto de , designado con :@0.293660:0.887211:0.930949:0.887211:0.930949:0.871499:0.293660:0.871499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.613553:0.887211:0.649834:0.887211:0.649834:0.871776:0.613553:0.871776:0.000000:0.000000:0.000000 R:@0.794682:0.886352:0.807972:0.886352:0.807972:0.873454:0.794682:0.873454:0.000000 [ , ] y definido como: :@0.317380:0.903853:0.482678:0.903853:0.482678:0.888141:0.317380:0.888141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.322185:0.903853:0.347697:0.903853:0.347697:0.888418:0.322185:0.888418:0.000000:0.000000:0.000000 [ , ] {:@0.353907:0.929430:0.416959:0.929430:0.416959:0.913717:0.353907:0.913717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.358700:0.929430:0.384212:0.929430:0.384212:0.913994:0.358700:0.913994:0.000000:0.000000:0.000000 5:@0.392882:0.928875:0.408215:0.928875:0.408215:0.915159:0.392882:0.915159:0.000000 x :@0.416867:0.929430:0.427561:0.929430:0.427561:0.913994:0.416867:0.913994:0.000000:0.000000 | } :@0.459660:0.929430:0.556255:0.929430:0.556255:0.913717:0.459660:0.913717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.463482:0.929430:0.472741:0.929430:0.472741:0.913994:0.463482:0.913994:0.000000 # #:@0.476625:0.928875:0.522496:0.928875:0.522496:0.915159:0.476625:0.915159:0.000000:0.000000:0.000000 x:@0.495824:0.929430:0.503279:0.929430:0.503279:0.913994:0.495824:0.913994:0.000000 b:@0.526361:0.929430:0.535620:0.929430:0.535620:0.913994:0.526361:0.913994:0.000000 a:@0.607969:0.937135:0.617649:0.937135:0.617649:0.920998:0.607969:0.920998:0.000000 b:@0.771869:0.937135:0.781549:0.937135:0.781549:0.920998:0.771869:0.920998:0.000000 [:@0.681076:0.937135:0.686176:0.937135:0.686176:0.920708:0.681076:0.920708:0.000000 a, b:@0.686176:0.937135:0.712482:0.937135:0.712482:0.920998:0.686176:0.920998:0.000000:0.000000:0.000000:0.000000 ]:@0.712482:0.937135:0.717582:0.937135:0.717582:0.920708:0.712482:0.920708:0.000000 Tema 2. Orden en el conjunto de los número reales:@0.073089:0.098522:0.819848:0.098522:0.819848:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.082576:0.289604:0.089353:0.289604:0.089353:0.275572:0.082576:0.275572:0.000000 0, 0, entonces :@0.089293:0.289604:0.232210:0.289604:0.232210:0.275320:0.089293:0.275320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.092891:0.289100:0.106830:0.289100:0.106830:0.276631:0.092891:0.276631:0.000000 y:@0.124852:0.289604:0.131646:0.289604:0.131646:0.275572:0.124852:0.275572:0.000000 .:@0.135177:0.289100:0.149116:0.289100:0.149116:0.276631:0.135177:0.276631:0.000000 x:@0.082582:0.304733:0.089360:0.304733:0.089360:0.290701:0.082582:0.290701:0.000000 0;:@0.089293:0.304733:0.149133:0.304733:0.149133:0.290449:0.089293:0.290449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 .:@0.092891:0.304229:0.134608:0.304229:0.134608:0.291760:0.092891:0.291760:0.000000:0.000000:0.000000 y:@0.110344:0.304733:0.117138:0.304733:0.117138:0.290701:0.110344:0.290701:0.000000 x :@0.082582:0.319862:0.092305:0.319862:0.092305:0.305830:0.082582:0.305830:0.000000:0.000000 .:@0.092255:0.319358:0.106194:0.319358:0.106194:0.306889:0.092255:0.306889:0.000000 0, 0, entonces :@0.106110:0.319862:0.235028:0.319862:0.235028:0.305578:0.106110:0.305578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.124216:0.319862:0.131010:0.319862:0.131010:0.305830:0.124216:0.305830:0.000000 .:@0.134541:0.319358:0.148480:0.319358:0.148480:0.306889:0.134541:0.306889:0.000000 xy:@0.082582:0.334991:0.096271:0.334991:0.096271:0.320959:0.082582:0.320959:0.000000:0.000000 0;:@0.096221:0.334991:0.128283:0.334991:0.128283:0.320707:0.096221:0.320707:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.099818:0.334487:0.113758:0.334487:0.113758:0.322018:0.099818:0.322018:0.000000 x:@0.082599:0.350120:0.089376:0.350120:0.089376:0.336088:0.082599:0.336088:0.000000 0, 0, entonces :@0.089309:0.350120:0.235681:0.350120:0.235681:0.335836:0.089309:0.335836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.092907:0.349616:0.106847:0.349616:0.106847:0.337147:0.092907:0.337147:0.000000 y:@0.124869:0.350120:0.131663:0.350120:0.131663:0.336088:0.124869:0.336088:0.000000 ,:@0.135194:0.349616:0.149133:0.349616:0.149133:0.337147:0.135194:0.337147:0.000000 x:@0.082599:0.365249:0.089376:0.365249:0.089376:0.351217:0.082599:0.351217:0.000000 0.:@0.089309:0.365249:0.149150:0.365249:0.149150:0.350965:0.089309:0.350965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 ,:@0.092907:0.364745:0.134625:0.364745:0.134625:0.352276:0.092907:0.352276:0.000000:0.000000:0.000000 y:@0.110361:0.365249:0.117155:0.365249:0.117155:0.351217:0.110361:0.351217:0.000000 Sean , . El par de :@0.082599:0.380378:0.238576:0.380378:0.238576:0.366094:0.082599:0.366094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.118426:0.380378:0.138356:0.380378:0.138356:0.366346:0.118426:0.366346:0.000000:0.000000:0.000000 [:@0.141887:0.380252:0.155827:0.380252:0.155827:0.367481:0.141887:0.367481:0.000000 R:@0.159341:0.379596:0.171423:0.379596:0.171423:0.367872:0.159341:0.367872:0.000000 desigualdades :@0.082599:0.395507:0.185161:0.395507:0.185161:0.381223:0.082599:0.381223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.082599:0.410636:0.089376:0.410636:0.089376:0.396604:0.082599:0.396604:0.000000 ; da lugar a la :@0.089309:0.410636:0.244767:0.410636:0.244767:0.396352:0.089309:0.396352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.092907:0.410132:0.106847:0.410132:0.106847:0.397663:0.092907:0.397663:0.000000 y y:@0.110361:0.410636:0.130307:0.410636:0.130307:0.396604:0.110361:0.396604:0.000000:0.000000:0.000000 ,:@0.133838:0.410132:0.147778:0.410132:0.147778:0.397663:0.133838:0.397663:0.000000 z:@0.151292:0.410636:0.157868:0.410636:0.157868:0.396604:0.151292:0.396604:0.000000 desigualdad compuesta :@0.082599:0.425765:0.245805:0.425765:0.245805:0.411481:0.082599:0.411481:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.082599:0.440894:0.089376:0.440894:0.089376:0.426862:0.082599:0.426862:0.000000 , que se lee “y :@0.089309:0.440894:0.236069:0.440894:0.236069:0.426610:0.089309:0.426610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , ,:@0.092907:0.440390:0.134625:0.440390:0.134625:0.427921:0.092907:0.427921:0.000000:0.000000:0.000000 y:@0.110361:0.440894:0.117155:0.440894:0.117155:0.426862:0.110361:0.426862:0.000000 z:@0.138139:0.440894:0.144715:0.440894:0.144715:0.426862:0.138139:0.426862:0.000000 es mayor que menor :@0.082599:0.456023:0.243378:0.456023:0.243378:0.441739:0.082599:0.441739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.175355:0.456023:0.191804:0.456023:0.191804:0.441991:0.175355:0.441991:0.000000:0.000000:0.000000 que ”. Igualmente, la :@0.082599:0.471152:0.224685:0.471152:0.224685:0.456868:0.082599:0.456868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.112034:0.471152:0.118610:0.471152:0.118610:0.457120:0.112034:0.457120:0.000000 desigualdad compuesta :@0.082582:0.486281:0.249168:0.486281:0.249168:0.471996:0.082582:0.471996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.082582:0.501410:0.089360:0.501410:0.089360:0.487378:0.082582:0.487378:0.000000 se lee “ es :@0.089293:0.501410:0.220804:0.501410:0.220804:0.487125:0.089293:0.487125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . .:@0.092891:0.500905:0.134608:0.500905:0.134608:0.488437:0.092891:0.488437:0.000000:0.000000:0.000000 y:@0.110344:0.501410:0.117138:0.501410:0.117138:0.487378:0.110344:0.487378:0.000000 z:@0.138122:0.501410:0.144699:0.501410:0.144699:0.487378:0.138122:0.487378:0.000000 y:@0.192524:0.501410:0.199318:0.501410:0.199318:0.487378:0.192524:0.487378:0.000000 mayor que y menor que :@0.082566:0.516539:0.256012:0.516539:0.256012:0.502254:0.082566:0.502254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.157517:0.516539:0.164093:0.516539:0.164093:0.502506:0.157517:0.502506:0.000000 x:@0.082549:0.531668:0.089326:0.531668:0.089326:0.517635:0.082549:0.517635:0.000000 ”, que corresponde a las :@0.089259:0.531668:0.247642:0.531668:0.247642:0.517383:0.089259:0.517383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos desigualdades :@0.082549:0.546796:0.212722:0.546796:0.212722:0.532512:0.082549:0.532512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.082549:0.561925:0.089326:0.561925:0.089326:0.547893:0.082549:0.547893:0.000000 ; .:@0.089259:0.561925:0.160663:0.561925:0.160663:0.547641:0.089259:0.547641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.092857:0.561421:0.106796:0.561421:0.106796:0.548952:0.092857:0.548952:0.000000 y y:@0.110310:0.561925:0.130257:0.561925:0.130257:0.547893:0.110310:0.547893:0.000000:0.000000:0.000000 .:@0.133788:0.561421:0.147727:0.561421:0.147727:0.548952:0.133788:0.548952:0.000000 z:@0.151242:0.561925:0.157818:0.561925:0.157818:0.547893:0.151242:0.547893:0.000000 Practica y escribe:@0.082549:0.584203:0.201058:0.584203:0.201058:0.569049:0.082549:0.569049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un :@0.200941:0.584203:0.225992:0.584203:0.225992:0.569919:0.200941:0.569919:0.000000:0.000000:0.000000:0.000000 ejemplo.:@0.082549:0.599332:0.139891:0.599332:0.139891:0.585047:0.082549:0.585047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Teorema:@0.082549:0.621609:0.142550:0.621609:0.142550:0.606455:0.082549:0.606455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.142540:0.621609:0.146205:0.621609:0.146205:0.607325:0.142540:0.607325:0.000000 Sean , . :@0.082549:0.636738:0.181128:0.636738:0.181128:0.622454:0.082549:0.622454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.118376:0.636738:0.141569:0.636738:0.141569:0.622706:0.118376:0.622706:0.000000:0.000000:0.000000 [:@0.145100:0.636612:0.159040:0.636612:0.159040:0.623841:0.145100:0.623841:0.000000 R:@0.162554:0.635956:0.174635:0.635956:0.174635:0.624231:0.162554:0.624231:0.000000 i) 0 :@0.082576:0.651866:0.162383:0.651866:0.162383:0.637581:0.082576:0.637581:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.101550:0.651866:0.109967:0.651866:0.109967:0.637834:0.101550:0.637834:0.000000 .:@0.113498:0.651361:0.127437:0.651361:0.127437:0.638893:0.113498:0.638893:0.000000 a:@0.162316:0.651866:0.170733:0.651866:0.170733:0.637834:0.162316:0.637834:0.000000 2:@0.170666:0.646059:0.178793:0.646059:0.178793:0.638790:0.170666:0.638790:0.000000 1:@0.178744:0.646353:0.183505:0.646353:0.183505:0.638025:0.178744:0.638025:0.000000 0.:@0.183463:0.651866:0.215525:0.651866:0.215525:0.637581:0.183463:0.637581:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.187060:0.651361:0.201000:0.651361:0.201000:0.638893:0.187060:0.638893:0.000000 ii) 0 :@0.082576:0.666995:0.162383:0.666995:0.162383:0.652710:0.082576:0.652710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.101550:0.666995:0.109967:0.666995:0.109967:0.652963:0.101550:0.652963:0.000000 ,:@0.113498:0.666490:0.127437:0.666490:0.127437:0.654022:0.113498:0.654022:0.000000 a:@0.162316:0.666995:0.170733:0.666995:0.170733:0.652963:0.162316:0.652963:0.000000 2:@0.170666:0.661188:0.178793:0.661188:0.178793:0.653919:0.170666:0.653919:0.000000 1:@0.178744:0.661482:0.183505:0.661482:0.183505:0.653154:0.178744:0.653154:0.000000 0.:@0.183463:0.666995:0.215525:0.666995:0.215525:0.652710:0.183463:0.652710:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.187060:0.666490:0.201000:0.666490:0.201000:0.654022:0.187060:0.654022:0.000000 iii) 0 0 :@0.082576:0.682124:0.220911:0.682124:0.220911:0.667839:0.082576:0.667839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , ,:@0.113234:0.681619:0.156574:0.681619:0.156574:0.669151:0.113234:0.669151:0.000000:0.000000:0.000000 a:@0.130687:0.682124:0.139104:0.682124:0.139104:0.668091:0.130687:0.668091:0.000000 b:@0.160088:0.682124:0.168506:0.682124:0.168506:0.668091:0.160088:0.668091:0.000000 ,:@0.203391:0.681619:0.217330:0.681619:0.217330:0.669151:0.203391:0.669151:0.000000 b:@0.220844:0.682124:0.229262:0.682124:0.229262:0.668091:0.220844:0.668091:0.000000 2:@0.229193:0.676317:0.237320:0.676317:0.237320:0.669048:0.229193:0.669048:0.000000 1:@0.237271:0.676611:0.242032:0.676611:0.242032:0.668283:0.237271:0.668283:0.000000 :@0.242031:0.682124:0.249243:0.682124:0.249243:0.667839:0.242031:0.667839:0.000000:0.000000 ,:@0.101550:0.696748:0.115490:0.696748:0.115490:0.684279:0.101550:0.684279:0.000000 :@0.115406:0.697253:0.119071:0.697253:0.119071:0.682968:0.115406:0.682968:0.000000 a:@0.119004:0.697253:0.127421:0.697253:0.127421:0.683220:0.119004:0.683220:0.000000 2:@0.127353:0.691446:0.135480:0.691446:0.135480:0.684177:0.127353:0.684177:0.000000 1:@0.135431:0.691740:0.140192:0.691740:0.140192:0.683412:0.135431:0.683412:0.000000 .:@0.140149:0.697253:0.143060:0.697253:0.143060:0.682968:0.140149:0.682968:0.000000 Competencia :@0.078585:0.250848:0.177276:0.250848:0.177276:0.235442:0.078585:0.235442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078585:0.265977:0.167199:0.265977:0.167199:0.250571:0.078585:0.250571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En el contexto general, ¿qué significa la palabra orden? Y en el contexto de los :@0.293660:0.162175:0.867792:0.162175:0.867792:0.146462:0.293660:0.146462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números reales, ¿qué significa?:@0.293660:0.178817:0.516491:0.178817:0.516491:0.163104:0.293660:0.163104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 2 (Ev. 2) Argumenta de diversa maneras la necesidad de establecer relaciones y características en conjuntos de números.:@0.256096:0.971366:0.914923:0.971366:0.914923:0.959939:0.256096:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.128546:0.163232:0.136759:0.163232:0.136759:0.149540:0.128546:0.149540:0.000000 a b:@0.229302:0.148901:0.265199:0.148902:0.265199:0.135211:0.229302:0.135210:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.240453:0.148409:0.254054:0.148409:0.254054:0.136243:0.240453:0.136243:0.000000 b a:@0.229297:0.193734:0.265199:0.193734:0.265199:0.180043:0.229297:0.180043:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.240448:0.193242:0.254049:0.193242:0.254049:0.181076:0.240448:0.181076:0.000000 b:@0.177306:0.163232:0.185519:0.163232:0.185519:0.149540:0.177306:0.149540:0.000000 b:@0.080358:0.206207:0.088571:0.206207:0.088571:0.192515:0.080358:0.192515:0.000000 a:@0.129111:0.206207:0.137324:0.206207:0.137324:0.192515:0.129111:0.192515:0.000000 Aprende la siguiente :@0.084437:0.793843:0.224824:0.791073:0.224327:0.776794:0.083941:0.779564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 simbología::@0.084963:0.808967:0.161270:0.807462:0.160774:0.793182:0.084467:0.794688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Z:@0.085462:0.823310:0.096619:0.823090:0.096212:0.811369:0.085054:0.811589:0.000000 1:@0.096361:0.818068:0.104485:0.817908:0.104232:0.810641:0.096108:0.810802:0.000000 : enteros positivos:@0.104638:0.823713:0.222921:0.821379:0.222425:0.807100:0.104141:0.809434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Q:@0.085983:0.838433:0.099917:0.838158:0.099510:0.826437:0.085575:0.826712:0.000000 1:@0.099663:0.833137:0.107787:0.832977:0.107535:0.825710:0.099411:0.825870:0.000000 : racionales positivos:@0.107940:0.838781:0.242731:0.836122:0.242234:0.821842:0.107444:0.824502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.086508:0.853557:0.098586:0.853318:0.098178:0.841597:0.086101:0.841836:0.000000 1:@0.098332:0.848297:0.106456:0.848137:0.106203:0.840870:0.098080:0.841030:0.000000 : reales positivos:@0.106609:0.853942:0.213172:0.851839:0.212676:0.837560:0.106112:0.839662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Z:@0.087034:0.868680:0.098191:0.868460:0.097784:0.856739:0.086626:0.856959:0.000000 1:@0.097938:0.863439:0.106062:0.863279:0.105809:0.856012:0.097685:0.856172:0.000000 :@0.106215:0.869085:0.109761:0.869015:0.109234:0.853866:0.105688:0.853936:0.000000 , :@0.109690:0.868890:0.127723:0.868534:0.127279:0.855767:0.109246:0.856123:0.000000:0.000000 Q:@0.127616:0.867880:0.141551:0.867606:0.141143:0.855885:0.127209:0.856160:0.000000 1:@0.141288:0.862584:0.149412:0.862424:0.149159:0.855157:0.141036:0.855317:0.000000 :@0.149566:0.868229:0.170442:0.867817:0.169916:0.852668:0.149039:0.853080:0.000000:0.000000:0.000000 ,:@0.153041:0.868034:0.166975:0.867759:0.166531:0.854992:0.152597:0.855267:0.000000 R:@0.170348:0.867037:0.182426:0.866798:0.182019:0.855077:0.169941:0.855316:0.000000 1:@0.182159:0.861777:0.190283:0.861617:0.190030:0.854350:0.181907:0.854510:0.000000 Simbología matemática:@0.083169:0.775280:0.253476:0.775280:0.253476:0.759874:0.083169:0.759874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@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