17:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento numérico y variacional:@0.603717:0.043661:0.926913:0.043661:0.926913:0.024916:0.603717:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 1 (Ev. 4) Interpreta y justifica cálculos numéricos al solucionar problemas.:@0.085171:0.970470:0.492412:0.970470:0.492412:0.959042:0.085171:0.959042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Producto:@0.073091:0.136836:0.143094:0.136836:0.143094:0.120167:0.073091:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Conmutativa: para todo , :@0.073091:0.164199:0.313038:0.164199:0.313038:0.147530:0.073091:0.147530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.205319:0.164199:0.209129:0.164199:0.209129:0.147252:0.205319:0.147252:0.000000 x y:@0.286808:0.164199:0.309209:0.164199:0.309209:0.148764:0.286808:0.148764:0.000000:0.000000:0.000000 [:@0.312971:0.163909:0.327607:0.163909:0.327607:0.150500:0.312971:0.150500:0.000000 :@0.327519:0.164558:0.336217:0.164558:0.336217:0.150076:0.327519:0.150076:0.000000:0.000000 R:@0.336129:0.163221:0.348815:0.163221:0.348815:0.150910:0.336129:0.150910:0.000000 , = .:@0.348728:0.164199:0.408423:0.164199:0.408423:0.147530:0.348728:0.147530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xy:@0.356275:0.164199:0.371332:0.164199:0.371332:0.148764:0.356275:0.148764:0.000000:0.000000 yx:@0.389813:0.164199:0.404668:0.164199:0.404668:0.148764:0.389813:0.148764:0.000000:0.000000 2. Asociativa::@0.073091:0.187988:0.184240:0.187988:0.184240:0.171319:0.073091:0.171319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.184117:0.187988:0.187927:0.187988:0.187927:0.171041:0.184117:0.171041:0.000000 para todo:@0.187854:0.187988:0.258769:0.187988:0.258769:0.172276:0.187854:0.172276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , , :@0.258648:0.187988:0.303414:0.187988:0.303414:0.171319:0.258648:0.171319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.262477:0.187988:0.299586:0.187988:0.299586:0.172553:0.262477:0.172553:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.303361:0.187698:0.317997:0.187698:0.317997:0.174289:0.303361:0.174289:0.000000 :@0.317909:0.188347:0.326607:0.188347:0.326607:0.173865:0.317909:0.173865:0.000000:0.000000 R:@0.326519:0.187010:0.339205:0.187010:0.339205:0.174699:0.326519:0.174699:0.000000 , = .:@0.339116:0.187988:0.447424:0.187988:0.447424:0.171319:0.339116:0.171319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.346663:0.187988:0.381140:0.187988:0.381140:0.172553:0.346663:0.172553:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.357873:0.187988:0.385944:0.187988:0.385944:0.172276:0.357873:0.172276:0.000000:0.000000:0.000000 (:@0.404407:0.187988:0.409284:0.187988:0.409284:0.172276:0.404407:0.172276:0.000000 x y z:@0.409211:0.187988:0.443688:0.187988:0.443688:0.172553:0.409211:0.172553:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.427821:0.187988:0.432698:0.187988:0.432698:0.172276:0.427821:0.172276:0.000000 3. Existencia de elemento unidad::@0.073091:0.211779:0.340094:0.211779:0.340094:0.195109:0.073091:0.195109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.339904:0.211779:0.343714:0.211779:0.343714:0.194832:0.339904:0.194832:0.000000 existe 1:@0.343641:0.211779:0.398174:0.211779:0.398174:0.196066:0.343641:0.196066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.398053:0.211779:0.401955:0.211779:0.401955:0.195109:0.398053:0.195109:0.000000 [:@0.401871:0.211489:0.416508:0.211489:0.416508:0.198079:0.401871:0.198079:0.000000 :@0.416420:0.212137:0.420812:0.212137:0.420812:0.197655:0.416420:0.197655:0.000000 R:@0.420725:0.210800:0.433411:0.210800:0.433411:0.198489:0.420725:0.198489:0.000000 , tal que para todo:@0.433323:0.211779:0.565424:0.211779:0.565424:0.196066:0.433323:0.196066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073091:0.235568:0.076993:0.235568:0.076993:0.218898:0.073091:0.218898:0.000000 x :@0.103212:0.235568:0.113907:0.235568:0.113907:0.220132:0.103212:0.220132:0.000000:0.000000 [:@0.113848:0.235278:0.128484:0.235278:0.128484:0.221868:0.113848:0.221868:0.000000 :@0.128396:0.235926:0.132789:0.235926:0.132789:0.221444:0.128396:0.221444:0.000000 R:@0.132701:0.234589:0.145387:0.234589:0.145387:0.222278:0.132701:0.222278:0.000000 , :@0.145299:0.235568:0.152938:0.235568:0.152938:0.218898:0.145299:0.218898:0.000000:0.000000 x:@0.152846:0.235568:0.160301:0.235568:0.160301:0.220132:0.152846:0.220132:0.000000 1:@0.160228:0.235568:0.183163:0.235568:0.183163:0.219855:0.160228:0.219855:0.000000:0.000000:0.000000:0.000000 ?:@0.164185:0.235013:0.170315:0.235013:0.170315:0.221297:0.164185:0.221297:0.000000 = = .:@0.183071:0.235568:0.261320:0.235568:0.261320:0.218898:0.183071:0.218898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.201607:0.235568:0.210590:0.235568:0.210590:0.219855:0.201607:0.219855:0.000000 ?:@0.214345:0.235013:0.220475:0.235013:0.220475:0.221297:0.214345:0.221297:0.000000 x:@0.224211:0.235568:0.231666:0.235568:0.231666:0.220132:0.224211:0.220132:0.000000 x:@0.250129:0.235568:0.257584:0.235568:0.257584:0.220132:0.250129:0.220132:0.000000 4. :@0.073091:0.259357:0.089363:0.259357:0.089363:0.242687:0.073091:0.242687:0.000000:0.000000:0.000000 Existencia de opuestos multiplicativos: para cada:@0.103212:0.259357:0.524340:0.259357:0.524340:0.243644:0.103212:0.243644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.525033:0.259357:0.528935:0.259357:0.528935:0.242687:0.525033:0.242687:0.000000 x:@0.535322:0.259357:0.542777:0.259357:0.542777:0.243921:0.535322:0.243921:0.000000 :@0.543301:0.259715:0.547694:0.259715:0.547694:0.245233:0.543301:0.245233:0.000000 [:@0.555302:0.259067:0.569938:0.259067:0.569938:0.245657:0.555302:0.245657:0.000000 :@0.571133:0.259715:0.575525:0.259715:0.575525:0.245233:0.571133:0.245233:0.000000 R:@0.583133:0.258378:0.595819:0.258378:0.595819:0.246067:0.583133:0.246067:0.000000 :@0.596998:0.259357:0.600901:0.259357:0.600901:0.242687:0.596998:0.242687:0.000000 con:@0.607288:0.259357:0.636611:0.259357:0.636611:0.243644:0.607288:0.243644:0.000000:0.000000:0.000000 :@0.637347:0.259357:0.659528:0.259357:0.659528:0.242687:0.637347:0.242687:0.000000:0.000000:0.000000 x:@0.647637:0.259357:0.655092:0.259357:0.655092:0.243921:0.647637:0.243921:0.000000 ±:@0.665915:0.259898:0.681248:0.259898:0.681248:0.244726:0.665915:0.244726:0.000000 0, :@0.682132:0.259357:0.710269:0.259357:0.710269:0.242687:0.682132:0.242687:0.000000:0.000000:0.000000:0.000000 :@0.706356:0.259357:0.710258:0.259357:0.710258:0.242687:0.706356:0.242687:0.000000 existe:@0.103224:0.281005:0.144890:0.281005:0.144890:0.265292:0.103224:0.265292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.144787:0.281005:0.207707:0.281004:0.207707:0.264334:0.144787:0.264335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.148616:0.281005:0.156071:0.281005:0.156071:0.265570:0.148616:0.265570:0.000000 –1:@0.155982:0.274940:0.166810:0.274940:0.166810:0.265221:0.155982:0.265221:0.000000:0.000000 5:@0.170591:0.280449:0.185924:0.280449:0.185924:0.266733:0.170591:0.266733:0.000000 1:@0.192070:0.273162:0.201462:0.273162:0.201462:0.256735:0.192070:0.256735:0.000000 x:@0.192879:0.289545:0.200673:0.289545:0.200673:0.273408:0.192879:0.273408:0.000000 [:@0.207628:0.280714:0.222264:0.280714:0.222264:0.267304:0.207628:0.267304:0.000000 :@0.222176:0.281362:0.226569:0.281362:0.226569:0.266880:0.222176:0.266880:0.000000 R:@0.226481:0.280025:0.239167:0.280025:0.239167:0.267714:0.226481:0.267714:0.000000 , tal que:@0.239079:0.281004:0.296381:0.281004:0.296381:0.265291:0.239079:0.265291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.296252:0.281004:0.437061:0.281004:0.437061:0.264334:0.296252:0.264334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.300081:0.281004:0.328612:0.281004:0.328612:0.265568:0.300081:0.265568:0.000000:0.000000:0.000000 ?:@0.311291:0.280449:0.317421:0.280449:0.317421:0.266733:0.311291:0.266733:0.000000 –1:@0.328530:0.274940:0.339358:0.274940:0.339358:0.265221:0.328530:0.265221:0.000000:0.000000 5:@0.343139:0.280449:0.358472:0.280449:0.358472:0.266733:0.343139:0.266733:0.000000 x:@0.362209:0.281004:0.369664:0.281004:0.369664:0.265568:0.362209:0.265568:0.000000 –1:@0.369587:0.274940:0.380415:0.274940:0.380415:0.265221:0.369587:0.265221:0.000000:0.000000 ? 5:@0.384195:0.280449:0.420605:0.280449:0.420605:0.266733:0.384195:0.266733:0.000000:0.000000:0.000000 x:@0.394062:0.281004:0.401517:0.281004:0.401517:0.265568:0.394062:0.265568:0.000000 1:@0.424342:0.281004:0.433324:0.281004:0.433324:0.265291:0.424342:0.265291:0.000000 En caso de confusión, se utilizará la notación :@0.073113:0.304788:0.398792:0.304788:0.398792:0.289075:0.073113:0.289075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.073113:0.321429:0.101124:0.321435:0.101124:0.305999:0.073113:0.305994:0.000000:0.000000:0.000000 3:@0.082284:0.319821:0.092041:0.319821:0.092041:0.311093:0.082284:0.311093:0.000000 , caso contrario se escribirá o también :@0.101050:0.321435:0.400205:0.321435:0.400205:0.305722:0.101050:0.305722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ab:@0.298744:0.321435:0.317188:0.321435:0.317188:0.305999:0.298744:0.305999:0.000000:0.000000 a.b:@0.400058:0.321435:0.421760:0.321435:0.421760:0.305999:0.400058:0.305999:0.000000:0.000000:0.000000 Las propiedades, de la 1 a la 4, descritas para el producto de números reales, dan la :@0.073090:0.348796:0.710018:0.348796:0.710018:0.333084:0.073090:0.333084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estructura algebraica del grupo conmutativo. Escribimos (:@0.073090:0.365438:0.497300:0.365438:0.497300:0.349726:0.073090:0.349726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.497423:0.364461:0.510109:0.364461:0.510109:0.352150:0.497423:0.352150:0.000000 2:@0.510093:0.364885:0.525426:0.364885:0.525426:0.351169:0.510093:0.351169:0.000000 {0}, ) y lo denominamos :@0.525407:0.365440:0.710327:0.365440:0.710327:0.349727:0.525407:0.349727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.551711:0.365440:0.559166:0.365440:0.559166:0.350004:0.551711:0.350004:0.000000 grupo conmutativo del producto de números reales:@0.073086:0.382081:0.465948:0.382081:0.465948:0.365412:0.073086:0.365412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.465694:0.382081:0.468897:0.382081:0.468897:0.366369:0.465694:0.366369:0.000000 Las operaciones de adición y producto están relacionadas con la propiedad distributiva: :@0.073086:0.409443:0.710873:0.409443:0.710873:0.393731:0.073086:0.393731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para todo , , :@0.073086:0.426085:0.191886:0.426085:0.191886:0.410373:0.073086:0.410373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.147819:0.426085:0.183971:0.426085:0.183971:0.410650:0.147819:0.410650:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.191836:0.425796:0.206472:0.425796:0.206472:0.412387:0.191836:0.412387:0.000000 :@0.206385:0.426445:0.210777:0.426445:0.210777:0.411963:0.206385:0.411963:0.000000 R:@0.210689:0.425108:0.223375:0.425108:0.223375:0.412797:0.210689:0.412797:0.000000 ; ( + ) = + .:@0.223288:0.426086:0.351034:0.426086:0.351034:0.410374:0.223288:0.410374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.230356:0.426086:0.250015:0.426086:0.250015:0.410651:0.230356:0.410651:0.000000:0.000000:0.000000 z:@0.268735:0.426086:0.275969:0.426086:0.275969:0.410651:0.268735:0.410651:0.000000 xy:@0.299475:0.426086:0.314532:0.426086:0.314532:0.410651:0.299475:0.410651:0.000000:0.000000 xz:@0.333271:0.426086:0.347886:0.426086:0.347886:0.410651:0.333271:0.410651:0.000000:0.000000 1.4 Propiedades algebraicas de los números reales:@0.073084:0.453448:0.467517:0.453448:0.467517:0.436501:0.073084:0.436501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.5 Productos notables y factorización:@0.073084:0.648477:0.372499:0.648477:0.372499:0.631530:0.073084:0.631530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicio resuelto:@0.073084:0.675839:0.201666:0.675839:0.201666:0.659169:0.073084:0.659169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Consideremos tres números reales positivos :@0.073091:0.703207:0.422188:0.703207:0.422188:0.687494:0.073091:0.687494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a, b :@0.421683:0.703207:0.449551:0.703207:0.449551:0.687772:0.421683:0.687772:0.000000:0.000000:0.000000:0.000000:0.000000 y , tales que y son los lados del rectángulo :@0.103219:0.719849:0.450321:0.719849:0.450321:0.704136:0.103219:0.704136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.115717:0.719849:0.123375:0.719849:0.123375:0.704414:0.115717:0.704414:0.000000 a c:@0.202029:0.719849:0.235825:0.719849:0.235825:0.704414:0.202029:0.704414:0.000000:0.000000:0.000000 R:@0.103200:0.736491:0.112146:0.736491:0.112146:0.721055:0.103200:0.721055:0.000000 1:@0.112743:0.739663:0.117980:0.739663:0.117980:0.730503:0.112743:0.730503:0.000000 , mientras que y son los lados del :@0.118395:0.736491:0.450351:0.736491:0.450351:0.720778:0.118395:0.720778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.248994:0.736491:0.258253:0.736491:0.258253:0.721055:0.248994:0.721055:0.000000 c:@0.285072:0.736491:0.292730:0.736491:0.292730:0.721055:0.285072:0.721055:0.000000 rectángulo , como se ilustra en la Figura 1.2.:@0.103209:0.753133:0.432623:0.753133:0.432623:0.737420:0.103209:0.737420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.186318:0.753133:0.195263:0.753133:0.195263:0.737697:0.186318:0.737697:0.000000 2:@0.195196:0.756305:0.200433:0.756305:0.200433:0.747144:0.195196:0.747144:0.000000 Da lugar a la región , la unión de y , :@0.073099:0.812932:0.377145:0.812932:0.377145:0.797220:0.073099:0.797220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.220744:0.812932:0.229690:0.812932:0.229690:0.797497:0.220744:0.797497:0.000000 R:@0.324690:0.812932:0.333636:0.812932:0.333636:0.797497:0.324690:0.797497:0.000000 1:@0.333621:0.816104:0.338857:0.816104:0.338857:0.806944:0.333621:0.806944:0.000000 R:@0.355761:0.812932:0.364707:0.812932:0.364707:0.797497:0.355761:0.797497:0.000000 2:@0.364685:0.816104:0.369922:0.816104:0.369922:0.806944:0.364685:0.806944:0.000000 que notamos :@0.073094:0.829574:0.178918:0.829574:0.178918:0.813861:0.073094:0.813861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R R R:@0.180556:0.829574:0.262838:0.829574:0.262838:0.814139:0.180556:0.814139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.194325:0.829019:0.209658:0.829019:0.209658:0.815304:0.194325:0.815304:0.000000 1:@0.223649:0.832746:0.228886:0.832746:0.228886:0.823586:0.223649:0.823586:0.000000 ø:@0.233663:0.829435:0.248996:0.829435:0.248996:0.815387:0.233663:0.815387:0.000000 2:@0.262984:0.832746:0.267942:0.832746:0.267942:0.823748:0.262984:0.823748:0.000000 (véase Figura :@0.268039:0.829574:0.377122:0.829574:0.377122:0.813861:0.268039:0.813861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.2).:@0.073088:0.846216:0.102042:0.846216:0.102042:0.830503:0.073088:0.830503:0.000000:0.000000:0.000000:0.000000:0.000000 El área de es y de es .:@0.073088:0.873578:0.297204:0.873579:0.297204:0.857866:0.073088:0.857865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.146588:0.873578:0.155534:0.873578:0.155534:0.858142:0.146588:0.858142:0.000000 1:@0.155467:0.876751:0.160704:0.876751:0.160704:0.867591:0.155467:0.867591:0.000000 ac:@0.184180:0.873579:0.201023:0.873579:0.201023:0.858144:0.184180:0.858144:0.000000:0.000000 R:@0.239623:0.873579:0.248569:0.873579:0.248569:0.858144:0.239623:0.858144:0.000000 2:@0.248500:0.876751:0.253737:0.876751:0.253737:0.867591:0.248500:0.867591:0.000000 bc:@0.277214:0.873579:0.294057:0.873579:0.294057:0.858144:0.277214:0.858144:0.000000:0.000000 El área de estos tres rectángulos es::@0.073078:0.890221:0.327433:0.890221:0.327433:0.874508:0.073078:0.874508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a(R) ac bc c(a b).:@0.073078:0.906863:0.260206:0.906863:0.260206:0.891427:0.073078:0.891427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.104020:0.906308:0.119353:0.906308:0.119353:0.892592:0.104020:0.892592:0.000000 1:@0.142547:0.906308:0.157880:0.906308:0.157880:0.892592:0.142547:0.892592:0.000000 5:@0.181073:0.906308:0.196406:0.906308:0.196406:0.892592:0.181073:0.892592:0.000000 1:@0.224404:0.906308:0.239737:0.906308:0.239737:0.892592:0.224404:0.892592:0.000000 Si 3,5 m; 4 m; y 2 m,:@0.406323:0.812933:0.642819:0.812933:0.642819:0.797221:0.406323:0.797221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.422503:0.812933:0.431761:0.812933:0.431761:0.797498:0.422503:0.797498:0.000000 5:@0.435645:0.812379:0.450979:0.812379:0.450979:0.798663:0.435645:0.798663:0.000000 b:@0.501783:0.812933:0.511041:0.812933:0.511041:0.797498:0.501783:0.797498:0.000000 5:@0.514925:0.812379:0.530259:0.812379:0.530259:0.798663:0.514925:0.798663:0.000000 c:@0.581007:0.812933:0.588665:0.812933:0.588665:0.797498:0.581007:0.797498:0.000000 5:@0.592549:0.812379:0.607882:0.812379:0.607882:0.798663:0.592549:0.798663:0.000000 calcula el área de cada rectángulo y :@0.406323:0.829575:0.710407:0.829575:0.710407:0.813863:0.406323:0.813863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 verifica que :@0.406323:0.846217:0.494000:0.846217:0.494000:0.830504:0.406323:0.830504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ac bc c(a b):@0.406323:0.873579:0.540751:0.873579:0.540751:0.858144:0.406323:0.858144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.426350:0.873024:0.441683:0.873024:0.441683:0.859309:0.426350:0.859309:0.000000 5:@0.464876:0.873024:0.480209:0.873024:0.480209:0.859309:0.464876:0.859309:0.000000 1:@0.508207:0.873024:0.523540:0.873024:0.523540:0.859309:0.508207:0.859309:0.000000 .:@0.540696:0.873579:0.543898:0.873579:0.543898:0.857866:0.540696:0.857866:0.000000 A(R ):@0.406323:0.890221:0.439896:0.890221:0.439896:0.874786:0.406323:0.874786:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.429827:0.893393:0.435064:0.893393:0.435064:0.884233:0.429827:0.884233:0.000000 3,5 2 7 m,:@0.439822:0.890221:0.570164:0.890221:0.570164:0.874508:0.439822:0.874508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.443780:0.889666:0.459113:0.889666:0.459113:0.875951:0.443780:0.875951:0.000000 3 5:@0.487847:0.889666:0.535227:0.889666:0.535227:0.875951:0.487847:0.875951:0.000000:0.000000:0.000000 A(R ):@0.406321:0.906863:0.439896:0.906863:0.439896:0.891428:0.406321:0.891427:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.429827:0.910036:0.435064:0.910036:0.435064:0.900875:0.429827:0.900875:0.000000 4 2 8 m,:@0.439822:0.906863:0.558144:0.906863:0.558144:0.891151:0.439822:0.891151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 3 5:@0.443780:0.906308:0.523207:0.906308:0.523207:0.892593:0.443780:0.892593:0.000000:0.000000:0.000000:0.000000:0.000000 A(R):@0.406321:0.923505:0.434686:0.923505:0.434686:0.908070:0.406321:0.908070:0.000000:0.000000:0.000000:0.000000 7 8 15 m,:@0.434650:0.923505:0.561881:0.923505:0.561881:0.907792:0.434650:0.907792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 1 5:@0.438607:0.922950:0.518035:0.922950:0.518035:0.909235:0.438607:0.909235:0.000000:0.000000:0.000000:0.000000:0.000000 A(R):@0.406339:0.940147:0.434705:0.940147:0.434705:0.924712:0.406339:0.924712:0.000000:0.000000:0.000000:0.000000 2(3,5 4) 2(7,5) 15 m.:@0.434668:0.940147:0.654966:0.940147:0.654966:0.924434:0.434668:0.924434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.438626:0.939592:0.453959:0.939592:0.453959:0.925877:0.438626:0.925877:0.000000 1:@0.496388:0.939592:0.511721:0.939592:0.511721:0.925877:0.496388:0.925877:0.000000 5:@0.533220:0.939592:0.548554:0.939592:0.548554:0.925877:0.533220:0.925877:0.000000 5:@0.595787:0.939592:0.611120:0.939592:0.611120:0.925877:0.595787:0.925877:0.000000 Ley cancelativa:@0.134585:0.488254:0.249647:0.488254:0.249647:0.471584:0.134585:0.471584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , , :@0.103918:0.515616:0.183437:0.515616:0.183437:0.499903:0.103918:0.499903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y z:@0.143328:0.515616:0.179480:0.515616:0.179480:0.500180:0.143328:0.500180:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.183387:0.515327:0.198024:0.515327:0.198024:0.501917:0.183387:0.501917:0.000000 :@0.197936:0.515976:0.202328:0.515976:0.202328:0.501493:0.197936:0.501493:0.000000 R:@0.202240:0.514639:0.214926:0.514639:0.214926:0.502327:0.202240:0.502327:0.000000 . Entonces,:@0.214839:0.515617:0.292007:0.515617:0.292007:0.499904:0.214839:0.499904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i) :@0.080201:0.532259:0.092810:0.532259:0.092810:0.516546:0.080201:0.516546:0.000000:0.000000:0.000000 x y x z:@0.108662:0.532259:0.203275:0.532259:0.203275:0.516824:0.108662:0.516824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 5 1:@0.119301:0.531704:0.192893:0.531704:0.192893:0.517988:0.119301:0.517988:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.203220:0.532259:0.214338:0.532259:0.214338:0.516546:0.203220:0.516546:0.000000:0.000000:0.000000 ⇔:@0.214246:0.531843:0.233426:0.531843:0.233426:0.514854:0.214246:0.514854:0.000000 :@0.233334:0.532259:0.237365:0.532259:0.237365:0.516546:0.233334:0.516546:0.000000 y z.:@0.237291:0.532259:0.276922:0.532259:0.276922:0.516824:0.237291:0.516824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.247949:0.531704:0.263282:0.531704:0.263282:0.517988:0.247949:0.517988:0.000000 ii) Si:@0.080201:0.548901:0.120991:0.548901:0.120991:0.533188:0.080201:0.533188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x 0 xy xz:@0.120888:0.548901:0.220103:0.548901:0.220103:0.533465:0.120888:0.533465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ±:@0.134767:0.549442:0.150101:0.549442:0.150101:0.534270:0.134767:0.534270:0.000000 ; :@0.161697:0.548901:0.168858:0.548901:0.168858:0.533188:0.161697:0.533188:0.000000:0.000000 5:@0.187007:0.548346:0.202340:0.548346:0.202340:0.534630:0.187007:0.534630:0.000000 :@0.220048:0.548901:0.224079:0.548901:0.224079:0.533188:0.220048:0.533188:0.000000 ⇔:@0.224006:0.548485:0.243186:0.548485:0.243186:0.531496:0.224006:0.531496:0.000000 :@0.243094:0.548901:0.247125:0.548901:0.247125:0.533188:0.243094:0.533188:0.000000 y z.:@0.247052:0.548901:0.286682:0.548901:0.286682:0.533465:0.247052:0.533465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.257709:0.548346:0.273043:0.548346:0.273043:0.534630:0.257709:0.534630:0.000000 Sean , :@0.317386:0.488255:0.371337:0.488255:0.371337:0.472542:0.317386:0.472542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.356796:0.488255:0.378719:0.488255:0.378719:0.472820:0.356796:0.472820:0.000000:0.000000:0.000000 :@0.378653:0.488612:0.401899:0.488612:0.401899:0.474130:0.378653:0.474130:0.000000:0.000000:0.000000 [:@0.382958:0.487964:0.397594:0.487964:0.397594:0.474554:0.382958:0.474554:0.000000 R:@0.401811:0.487275:0.414497:0.487275:0.414497:0.474964:0.401811:0.474964:0.000000 . Se verifican las igualdades.:@0.414408:0.488254:0.612958:0.488254:0.612958:0.472541:0.414408:0.472541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i) :@0.317374:0.504896:0.329983:0.504896:0.329983:0.489183:0.317374:0.489183:0.000000:0.000000:0.000000 x:@0.345835:0.504896:0.353290:0.504896:0.353290:0.489460:0.345835:0.489460:0.000000 (:@0.353216:0.504896:0.362051:0.504896:0.362051:0.489183:0.353216:0.489183:0.000000:0.000000 2 5 2:@0.361959:0.504341:0.428023:0.504341:0.428023:0.490625:0.361959:0.490625:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.377201:0.504896:0.392718:0.504896:0.392718:0.489460:0.377201:0.489460:0.000000:0.000000:0.000000 ):@0.384600:0.504896:0.389478:0.504896:0.389478:0.489183:0.384600:0.489183:0.000000 (:@0.407886:0.504896:0.412763:0.504896:0.412763:0.489183:0.407886:0.489183:0.000000 x y xy.:@0.427931:0.504896:0.505396:0.504896:0.505396:0.489460:0.427931:0.489460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.435312:0.504896:0.440190:0.504896:0.440190:0.489183:0.435312:0.489183:0.000000 5 2:@0.454014:0.504341:0.487828:0.504341:0.487828:0.490625:0.454014:0.490625:0.000000:0.000000:0.000000 ii) (:@0.317374:0.521537:0.350728:0.521537:0.350728:0.505825:0.317374:0.505825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.350632:0.520983:0.365965:0.520983:0.365965:0.507267:0.350632:0.507267:0.000000 x :@0.365873:0.521537:0.381372:0.521537:0.381372:0.506102:0.365873:0.506102:0.000000:0.000000:0.000000 ) (:@0.373255:0.521537:0.386177:0.521537:0.386177:0.505825:0.373255:0.505825:0.000000:0.000000:0.000000 2 5:@0.386103:0.520983:0.432121:0.520983:0.432121:0.507267:0.386103:0.507267:0.000000:0.000000:0.000000 y xy.:@0.401344:0.521537:0.452929:0.521537:0.452929:0.506102:0.401344:0.506102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.408744:0.521537:0.413622:0.521537:0.413622:0.505825:0.408744:0.505825:0.000000 Las propiedades i y ii se conocen como leyes de :@0.345828:0.538179:0.697064:0.538179:0.697064:0.522467:0.345828:0.522467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los signos.:@0.345828:0.554821:0.419774:0.554821:0.419774:0.539108:0.345828:0.539108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , :@0.080201:0.584116:0.143209:0.584116:0.143209:0.569117:0.080201:0.569117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.118206:0.584116:0.139361:0.584116:0.139361:0.569382:0.118206:0.569382:0.000000:0.000000:0.000000 [:@0.143209:0.583983:0.157845:0.583983:0.157845:0.570573:0.143209:0.570573:0.000000 :@0.157845:0.584632:0.162238:0.584632:0.162238:0.570150:0.157845:0.570150:0.000000 R:@0.162238:0.583295:0.174924:0.583295:0.174924:0.570984:0.162238:0.570984:0.000000 . :@0.174924:0.584116:0.181267:0.584116:0.181267:0.569382:0.174924:0.569382:0.000000:0.000000 Entonces,:@0.181267:0.584116:0.248736:0.584116:0.248736:0.569117:0.181267:0.569117:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 xy 0:@0.080201:0.603575:0.123723:0.603575:0.123723:0.588842:0.080201:0.588842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.097806:0.603046:0.112443:0.603046:0.112443:0.589954:0.097806:0.589954:0.000000 :@0.123723:0.603575:0.127571:0.603575:0.127571:0.588577:0.123723:0.588577:0.000000 ⇔:@0.127571:0.603178:0.145879:0.603178:0.145879:0.586962:0.127571:0.586962:0.000000 :@0.145879:0.603575:0.149727:0.603575:0.149727:0.588577:0.145879:0.588577:0.000000 x 0 y 0.:@0.149727:0.603575:0.242922:0.603575:0.242922:0.588842:0.149727:0.588842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.160006:0.603046:0.174643:0.603046:0.174643:0.589954:0.160006:0.589954:0.000000 :@0.185923:0.603575:0.189771:0.603575:0.189771:0.588577:0.185923:0.588577:0.000000 ∨:@0.189771:0.603178:0.200366:0.603178:0.200366:0.586962:0.189771:0.586962:0.000000 5:@0.213825:0.603046:0.228461:0.603046:0.228461:0.589954:0.213825:0.589954:0.000000 Sean :@0.317374:0.584746:0.356887:0.584746:0.356887:0.569033:0.317374:0.569033:0.000000:0.000000:0.000000:0.000000:0.000000 a, b, c, d:@0.356784:0.584746:0.410951:0.584746:0.410951:0.569311:0.356784:0.569311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.410938:0.584746:0.414969:0.584746:0.414969:0.569033:0.410938:0.569033:0.000000 [:@0.414895:0.584607:0.430229:0.584607:0.430229:0.570559:0.414895:0.570559:0.000000 :@0.430130:0.585105:0.434522:0.585105:0.434522:0.570623:0.430130:0.570623:0.000000 R:@0.434435:0.583768:0.447121:0.583768:0.447121:0.571457:0.434435:0.571457:0.000000 . :@0.447033:0.584746:0.453604:0.584746:0.453604:0.569311:0.447033:0.569311:0.000000:0.000000 Se verifican::@0.453549:0.584746:0.539067:0.584746:0.539067:0.569033:0.453549:0.569033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i) :@0.317374:0.601388:0.329983:0.601388:0.329983:0.585675:0.317374:0.585675:0.000000:0.000000:0.000000 a b – c ab – ac.:@0.345835:0.601388:0.479166:0.601388:0.479166:0.585953:0.345835:0.585953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.361518:0.601388:0.366396:0.601388:0.366396:0.585675:0.361518:0.585675:0.000000 ):@0.398737:0.601388:0.403615:0.601388:0.403615:0.585675:0.398737:0.585675:0.000000 5:@0.406781:0.600833:0.422114:0.600833:0.422114:0.587118:0.406781:0.587118:0.000000 ii) :@0.317374:0.618030:0.333756:0.618030:0.333756:0.602317:0.317374:0.602317:0.000000:0.000000:0.000000:0.000000 2 1:@0.345835:0.617475:0.393657:0.617475:0.393657:0.603759:0.345835:0.603759:0.000000:0.000000:0.000000 (:@0.361076:0.618030:0.365954:0.618030:0.365954:0.602317:0.361076:0.602317:0.000000 a b a b.:@0.365880:0.618030:0.490847:0.618030:0.490847:0.602595:0.365880:0.602595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.406008:0.618030:0.410886:0.618030:0.410886:0.602317:0.406008:0.602317:0.000000 5 2 2:@0.414052:0.617475:0.475551:0.617475:0.475551:0.603759:0.414052:0.603759:0.000000:0.000000:0.000000:0.000000:0.000000 c:@0.505469:0.711543:0.512082:0.711543:0.512082:0.698213:0.505469:0.698213:0.000000 a:@0.537745:0.749078:0.545742:0.749078:0.545742:0.735747:0.537745:0.735747:0.000000 b:@0.623127:0.749078:0.631123:0.749078:0.631123:0.735747:0.623127:0.735747:0.000000 a + b:@0.584729:0.759799:0.615919:0.759799:0.615919:0.746469:0.584729:0.746469:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.536211:0.712095:0.543937:0.712095:0.543937:0.698764:0.536211:0.698764:0.000000 1:@0.543939:0.714829:0.548220:0.714829:0.548220:0.707058:0.543939:0.707058:0.000000 R:@0.619698:0.712089:0.627424:0.712089:0.627424:0.698758:0.619698:0.698758:0.000000 2:@0.627424:0.714829:0.631706:0.714829:0.631706:0.707058:0.627424:0.707058:0.000000 Figura 1.2.:@0.652685:0.781509:0.706341:0.781509:0.706341:0.770082:0.652685:0.770082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. Se define resta de :@0.739544:0.174723:0.879272:0.174723:0.879272:0.160439:0.739544:0.160439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.749907:0.174723:0.757170:0.174723:0.757170:0.160439:0.749907:0.160439:0.000000:0.000000 números reales , :@0.758519:0.189852:0.903752:0.189852:0.903752:0.175568:0.758519:0.175568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.862687:0.189852:0.869464:0.189852:0.869464:0.175820:0.862687:0.175820:0.000000 2:@0.872995:0.189348:0.886934:0.189348:0.886934:0.176879:0.872995:0.176879:0.000000 y:@0.890448:0.189852:0.897242:0.189852:0.897242:0.175820:0.890448:0.175820:0.000000 que se lee menos , :@0.758519:0.204981:0.901677:0.204981:0.901677:0.190697:0.758519:0.190697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.828918:0.204981:0.835695:0.204981:0.835695:0.190949:0.828918:0.190949:0.000000 y:@0.888373:0.204981:0.895167:0.204981:0.895167:0.190949:0.888373:0.190949:0.000000 como::@0.758502:0.220110:0.800119:0.220110:0.800119:0.205825:0.758502:0.205825:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.739544:0.235239:0.765297:0.235239:0.765297:0.221207:0.739544:0.221207:0.000000:0.000000:0.000000 (:@0.765236:0.235239:0.846261:0.235239:0.846261:0.220954:0.765236:0.220954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5 1 2:@0.768833:0.234734:0.860117:0.234734:0.860117:0.222266:0.768833:0.222266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.786287:0.235239:0.793081:0.235239:0.793081:0.221207:0.786287:0.221207:0.000000 x:@0.814065:0.235239:0.820842:0.235239:0.820842:0.221207:0.814065:0.221207:0.000000 y:@0.860033:0.235239:0.866827:0.235239:0.866827:0.221207:0.860033:0.221207:0.000000 ).:@0.866760:0.235239:0.874039:0.235239:0.874039:0.220954:0.866760:0.220954:0.000000:0.000000 b. Si 0, se define la :@0.739544:0.250368:0.893491:0.250368:0.893491:0.236083:0.739544:0.236083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.773224:0.250368:0.780018:0.250368:0.780018:0.236335:0.773224:0.236335:0.000000 Þ:@0.783549:0.249863:0.797488:0.249863:0.797488:0.237395:0.783549:0.237395:0.000000 división de números :@0.758515:0.271800:0.896314:0.271800:0.896314:0.257516:0.758515:0.257516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 reales (que se lee :@0.758515:0.294494:0.904594:0.294494:0.904594:0.280209:0.758515:0.280209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.803598:0.283607:0.810714:0.283607:0.810714:0.268873:0.803598:0.268873:0.000000 y:@0.803580:0.299996:0.810714:0.299996:0.810714:0.285262:0.803580:0.285262:0.000000 x:@0.894152:0.294494:0.900929:0.294494:0.900929:0.280462:0.894152:0.280462:0.000000 dividido entre ) como :@0.758524:0.309623:0.911270:0.309623:0.911270:0.295338:0.758524:0.295338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.854141:0.309623:0.860935:0.309623:0.860935:0.295590:0.854141:0.295590:0.000000 se indica: :@0.758507:0.329795:0.822547:0.329795:0.822547:0.315510:0.758507:0.315510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.825995:0.322268:0.833111:0.322268:0.833111:0.307534:0.825995:0.307534:0.000000 y:@0.825977:0.338656:0.833111:0.338656:0.833111:0.323923:0.825977:0.323923:0.000000 :@0.836595:0.339880:0.840260:0.339880:0.840260:0.325596:0.836595:0.325596:0.000000 5:@0.840193:0.329290:0.854133:0.329290:0.854133:0.316821:0.840193:0.316821:0.000000 :@0.854049:0.329795:0.857714:0.329795:0.857714:0.315510:0.854049:0.315510:0.000000 xy:@0.857647:0.329795:0.871335:0.329795:0.871335:0.315762:0.857647:0.315762:0.000000:0.000000 2:@0.871268:0.323988:0.879395:0.323988:0.879395:0.316719:0.871268:0.316719:0.000000 1:@0.879346:0.324282:0.884107:0.324282:0.884107:0.315954:0.879346:0.315954:0.000000 .:@0.884063:0.329795:0.886974:0.329795:0.886974:0.315510:0.884063:0.315510:0.000000 El conjunto con las dos :@0.739549:0.359220:0.910971:0.359220:0.910971:0.344936:0.739549:0.344936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.818081:0.358439:0.830163:0.358439:0.830163:0.346714:0.818081:0.346714:0.000000 operaciones de adición :@0.739549:0.374349:0.897366:0.374349:0.897366:0.360065:0.739549:0.360065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y producto tiene una :@0.739549:0.389478:0.882103:0.389478:0.882103:0.375194:0.739549:0.375194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estructura algebraica de :@0.739549:0.404607:0.902498:0.404607:0.902498:0.390323:0.739549:0.390323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cuerpo, es decir que :@0.739549:0.419736:0.880147:0.419736:0.880147:0.405452:0.739549:0.405452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ; ) es grupo :@0.739549:0.434865:0.846304:0.434865:0.846304:0.420581:0.739549:0.420581:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.743917:0.434083:0.755998:0.434083:0.755998:0.422358:0.743917:0.422358:0.000000 1:@0.762341:0.434361:0.776280:0.434361:0.776280:0.421892:0.762341:0.421892:0.000000 conmutativo; (:@0.739549:0.449994:0.835394:0.449994:0.835394:0.435710:0.739549:0.435710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.835250:0.449212:0.847332:0.449212:0.847332:0.437487:0.835250:0.437487:0.000000 2:@0.847248:0.449490:0.861188:0.449490:0.861188:0.437021:0.847248:0.437021:0.000000 {0}, ) :@0.861104:0.449994:0.902754:0.449994:0.902754:0.435710:0.861104:0.435710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.887945:0.449994:0.894722:0.449994:0.894722:0.435962:0.887945:0.435962:0.000000 es grupo conmutativo y :@0.739549:0.465123:0.901151:0.465123:0.901151:0.450839:0.739549:0.450839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se satisface la propiedad :@0.739549:0.480252:0.903953:0.480252:0.903953:0.465968:0.739549:0.465968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 distributiva.:@0.739549:0.495381:0.816167:0.495381:0.816167:0.481097:0.739549:0.481097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Teorema:@0.739549:0.514078:0.801844:0.514078:0.801844:0.498671:0.739549:0.498671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. El elemento neutro “0” :@0.739544:0.529210:0.907306:0.529210:0.907306:0.514926:0.739544:0.514926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para la adición es único.:@0.758519:0.544339:0.915794:0.544339:0.915794:0.530055:0.758519:0.530055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b. El opuesto aditivo de :@0.739544:0.559468:0.911140:0.559468:0.911140:0.545184:0.739544:0.545184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.900698:0.559468:0.907475:0.559468:0.907475:0.545436:0.900698:0.545436:0.000000 es único.:@0.784516:0.574597:0.845923:0.574597:0.845923:0.560313:0.784516:0.560313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c. El elemento unidad :@0.739544:0.589726:0.891419:0.589726:0.891419:0.575442:0.739544:0.575442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 “1” para el producto es :@0.758519:0.604855:0.909567:0.604855:0.909567:0.590571:0.758519:0.590571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 único.:@0.758519:0.619984:0.798506:0.619984:0.798506:0.605700:0.758519:0.605700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d. El opuesto multiplicativo :@0.739544:0.635113:0.925764:0.635113:0.925764:0.620829:0.739544:0.620829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de :@0.758519:0.650242:0.782850:0.650242:0.782850:0.635958:0.758519:0.635958:0.000000:0.000000:0.000000:0.000000 x:@0.758519:0.665371:0.765296:0.665371:0.765296:0.651339:0.758519:0.651339:0.000000 :@0.765229:0.665371:0.768894:0.665371:0.768894:0.651087:0.765229:0.651087:0.000000 con 0 es :@0.794824:0.665371:0.888127:0.665371:0.888127:0.651087:0.794824:0.651087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.830714:0.665371:0.837491:0.665371:0.837491:0.651339:0.830714:0.651339:0.000000 Þ:@0.841022:0.664866:0.854961:0.664866:0.854961:0.652398:0.841022:0.652398:0.000000 único.:@0.758524:0.680500:0.798511:0.680500:0.798511:0.666215:0.758524:0.666215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.740294:0.139943:0.848854:0.139943:0.848854:0.122996:0.740294:0.122996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740294:0.156585:0.837769:0.156585:0.837769:0.139638:0.740294:0.139638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Aprende esta simbología::@0.747336:0.777308:0.915039:0.773999:0.914543:0.759719:0.746840:0.763028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.747857:0.792305:0.761792:0.792030:0.761348:0.779263:0.747413:0.779538:0.000000 : pertenece a:@0.761712:0.792158:0.847282:0.790470:0.846786:0.776190:0.761216:0.777879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.748360:0.806774:0.760438:0.806536:0.760030:0.794815:0.747953:0.795053:0.000000 : conjunto de números :@0.760381:0.807319:0.914083:0.804286:0.913587:0.790006:0.759885:0.793039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 reales:@0.767883:0.822305:0.805899:0.821555:0.805403:0.807275:0.767386:0.808025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R :@0.749411:0.837020:0.765588:0.836702:0.765180:0.824981:0.749003:0.825299:0.000000:0.000000 2:@0.768388:0.836923:0.782323:0.836648:0.781889:0.824184:0.767955:0.824459:0.000000 {0}: conjunto de :@0.782257:0.837154:0.890115:0.835026:0.889619:0.820747:0.781760:0.822875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 números reales :@0.768931:0.852551:0.873287:0.850492:0.872790:0.836213:0.768435:0.838272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 menos el cero.:@0.769457:0.867675:0.865315:0.865784:0.864818:0.851504:0.768961:0.853396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Simbología matemática:@0.746067:0.758743:0.916374:0.758743:0.916374:0.743337:0.746067:0.743337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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