16:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 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 Ejercicio resuelto:@0.293660:0.136836:0.422242:0.136836:0.422242:0.120167:0.293660:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Cómo se comprende el número real :@0.293660:0.164199:0.567341:0.164199:0.567341:0.148487:0.293660:0.148487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.576995:0.164479:0.586386:0.164479:0.586386:0.148052:0.576995:0.148052:0.000000 ?:@0.586849:0.164199:0.629204:0.164199:0.629204:0.148487:0.586849:0.148487:0.000000:0.000000:0.000000:0.000000:0.000000 1 p:@0.590807:0.163645:0.622283:0.163645:0.622283:0.149929:0.590807:0.149929:0.000000:0.000000:0.000000 • :@0.293660:0.195137:0.302164:0.195137:0.302164:0.179424:0.293660:0.179424:0.000000:0.000000 Una aproximación de 2 es 1,414 21 y una de es 3,141 59.:@0.323861:0.195137:0.756475:0.195137:0.756475:0.179424:0.323861:0.179424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.656984:0.194582:0.669262:0.194582:0.669262:0.180866:0.656984:0.180866:0.000000 Luego, :@0.322119:0.212791:0.375009:0.212791:0.375009:0.197078:0.322119:0.197078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.386101:0.212315:0.395492:0.212315:0.395492:0.195888:0.386101:0.195888:0.000000 se aproxima como la suma de 1,414 21 3,141 59 4,555 8.:@0.397224:0.212787:0.872098:0.212787:0.872098:0.197075:0.397224:0.197075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 p:@0.401182:0.212233:0.432658:0.212233:0.432658:0.198517:0.401182:0.198517:0.000000:0.000000:0.000000 1:@0.719636:0.212233:0.734969:0.212233:0.734969:0.198517:0.719636:0.198517:0.000000 5:@0.799803:0.212233:0.815136:0.212233:0.815136:0.198517:0.799803:0.198517:0.000000 • :@0.293660:0.244045:0.302164:0.244045:0.302164:0.228332:0.293660:0.228332:0.000000:0.000000 Otra aproximación de :@0.322201:0.244045:0.484220:0.244045:0.484220:0.228332:0.322201:0.228332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.495213:0.242472:0.504604:0.242472:0.504604:0.226045:0.495213:0.226045:0.000000 es 1,414 213 56 y la de es 3,141 592 65.:@0.506326:0.244045:0.805867:0.244045:0.805867:0.228332:0.506326:0.228332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.675691:0.243490:0.687969:0.243490:0.687969:0.229775:0.675691:0.229775:0.000000 Luego, :@0.322106:0.261020:0.374996:0.261020:0.374996:0.245307:0.322106:0.245307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.386101:0.259437:0.395492:0.259437:0.395492:0.243010:0.386101:0.243010:0.000000 se aproxima como la suma de:@0.397224:0.261021:0.637113:0.261021:0.637113:0.245308:0.397224:0.245308:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.401182:0.260466:0.416515:0.260466:0.416515:0.246750:0.401182:0.246750:0.000000 1,414 213 56 3,141 592 65 4,555 806 21.:@0.322123:0.278675:0.641663:0.278671:0.641663:0.262959:0.322123:0.262962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.415481:0.278117:0.430814:0.278117:0.430814:0.264401:0.415481:0.264401:0.000000 5:@0.528035:0.278117:0.543368:0.278117:0.543368:0.264401:0.528035:0.264401:0.000000 Así, :@0.322113:0.296326:0.351548:0.296326:0.351548:0.280613:0.322113:0.280613:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.364764:0.295848:0.374155:0.295848:0.374155:0.279421:0.364764:0.279421:0.000000 se interpreta como el único resultado de todas las aproximaciones :@0.376518:0.296322:0.930944:0.296322:0.930944:0.280609:0.376518:0.280609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 p:@0.382224:0.295767:0.412599:0.295767:0.412599:0.282051:0.382224:0.282051:0.000000:0.000000:0.000000 r s de :@0.322124:0.316500:0.433493:0.316494:0.433493:0.300781:0.322124:0.300787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.327469:0.319666:0.336258:0.319666:0.336258:0.310505:0.327469:0.310505:0.000000 1:@0.338432:0.315939:0.353765:0.315939:0.353765:0.302223:0.338432:0.302223:0.000000 m:@0.362679:0.319666:0.371468:0.319666:0.371468:0.310505:0.362679:0.310505:0.000000 [:@0.373641:0.316355:0.388975:0.316355:0.388975:0.302306:0.373641:0.302306:0.000000 Q :@0.391101:0.315634:0.410760:0.315634:0.410760:0.302736:0.391101:0.302736:0.000000:0.000000 2:@0.444641:0.314479:0.454032:0.314479:0.454032:0.298052:0.444641:0.298052:0.000000 , siendo:@0.455805:0.316494:0.545435:0.316494:0.545435:0.300781:0.455805:0.300781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1p:@0.459762:0.315939:0.489495:0.315939:0.489495:0.302223:0.459762:0.302223:0.000000:0.000000 r:@0.322118:0.336672:0.327401:0.336672:0.327401:0.321237:0.322118:0.321237:0.000000 m:@0.327337:0.339838:0.336126:0.339838:0.336126:0.330677:0.327337:0.330677:0.000000 una de tales aproximaciones de :@0.336079:0.336666:0.573667:0.336666:0.573667:0.320953:0.336079:0.320953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.583313:0.336601:0.592704:0.336601:0.592704:0.320174:0.583313:0.320174:0.000000 , al igual que:@0.595263:0.336666:0.690392:0.336666:0.690392:0.320953:0.595263:0.320953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 s:@0.322118:0.356844:0.328487:0.356844:0.328487:0.341408:0.322118:0.341408:0.000000 m:@0.328423:0.360010:0.337212:0.360010:0.337212:0.350849:0.328423:0.350849:0.000000 es una aproximación de .:@0.337165:0.356837:0.533791:0.356837:0.533791:0.341125:0.337165:0.341125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.518403:0.356283:0.530680:0.356283:0.530680:0.342567:0.518403:0.342567:0.000000 1.2 Operaciones en número reales :@0.293668:0.395682:0.581503:0.395682:0.581503:0.378735:0.293668:0.378735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.564402:0.394822:0.577692:0.394822:0.577692:0.381925:0.564402:0.381925:0.000000 En el conjunto de los números reales se introducen dos operaciones: adición “ ” y :@0.293668:0.423044:0.930946:0.423044:0.930946:0.407332:0.293668:0.407332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.575134:0.422184:0.588424:0.422184:0.588424:0.409287:0.575134:0.409287:0.000000 1:@0.894886:0.422490:0.910219:0.422490:0.910219:0.408774:0.894886:0.408774:0.000000 producto “ ”, que se definen a continuación.:@0.293650:0.440698:0.613375:0.440692:0.613375:0.424979:0.293650:0.424986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.371628:0.440137:0.377758:0.440137:0.377758:0.426422:0.371628:0.426422:0.000000 Adición: :@0.293667:0.468054:0.361993:0.468054:0.361993:0.451107:0.293667:0.451107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es la función denotada “ ” y definida como::@0.361903:0.468054:0.678647:0.468054:0.678647:0.452341:0.361903:0.452341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.535115:0.467499:0.550448:0.467499:0.550448:0.453784:0.535115:0.453784:0.000000 R:@0.330130:0.502817:0.344024:0.502817:0.344024:0.489333:0.330130:0.489333:0.000000 :@0.344024:0.503558:0.365505:0.503558:0.365505:0.487845:0.344024:0.487845:0.000000:0.000000:0.000000 3:@0.346325:0.503003:0.361658:0.503003:0.361658:0.489288:0.346325:0.489288:0.000000 R:@0.363775:0.502817:0.377669:0.502817:0.377669:0.489333:0.363775:0.489333:0.000000 .:@0.377669:0.503716:0.420679:0.503716:0.420679:0.487289:0.377669:0.487289:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.381883:0.503003:0.399225:0.503003:0.399225:0.486787:0.381883:0.486787:0.000000 R:@0.403436:0.502817:0.417330:0.502817:0.417330:0.489333:0.403436:0.489333:0.000000 (:@0.330136:0.528262:0.335235:0.528262:0.335235:0.511835:0.330136:0.511835:0.000000 x, y:@0.335235:0.528262:0.357789:0.528262:0.357789:0.512125:0.335235:0.512125:0.000000:0.000000:0.000000:0.000000 ) .:@0.357789:0.528262:0.431367:0.528261:0.431367:0.511834:0.357789:0.511835:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.367098:0.527549:0.384441:0.527549:0.384441:0.511332:0.367098:0.511332:0.000000 x:@0.388651:0.528261:0.396445:0.528261:0.396445:0.512124:0.388651:0.512124:0.000000 1:@0.400660:0.527549:0.415993:0.527549:0.415993:0.513833:0.400660:0.513833:0.000000 y:@0.420206:0.528261:0.428019:0.528261:0.428019:0.512124:0.420206:0.512124:0.000000 Nota que de la definición de la operación adición, se tiene , :@0.293660:0.553226:0.764026:0.553226:0.764026:0.537514:0.293660:0.537514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.719289:0.553226:0.741378:0.553226:0.741378:0.537791:0.719289:0.537791:0.000000:0.000000:0.000000 [:@0.745446:0.552936:0.760082:0.552936:0.760082:0.539526:0.745446:0.539526:0.000000 R:@0.762215:0.552248:0.774901:0.552248:0.774901:0.539937:0.762215:0.539937:0.000000 ⇒:@0.774813:0.552672:0.792155:0.552672:0.792155:0.536455:0.774813:0.536455:0.000000 x:@0.792065:0.553226:0.802907:0.553226:0.802907:0.537791:0.792065:0.537791:0.000000:0.000000 . En este :@0.802833:0.553226:0.930987:0.553226:0.930987:0.537514:0.802833:0.537514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.806956:0.552672:0.822290:0.552672:0.822290:0.538956:0.806956:0.538956:0.000000 y:@0.826321:0.553226:0.833794:0.553226:0.833794:0.537791:0.826321:0.537791:0.000000 [:@0.837844:0.552936:0.852480:0.552936:0.852480:0.539526:0.837844:0.539526:0.000000 R:@0.854613:0.552248:0.867299:0.552248:0.867299:0.539937:0.854613:0.539937:0.000000 caso, se dice que la suma de números reales es cerrada o conocida como propiedad :@0.293660:0.569868:0.931436:0.569868:0.931436:0.554155:0.293660:0.554155:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 clausurativa.:@0.293660:0.586510:0.382862:0.586510:0.382862:0.570797:0.293660:0.570797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Producto::@0.293660:0.614884:0.367400:0.614884:0.367400:0.598215:0.293660:0.598215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.367308:0.614884:0.371118:0.614884:0.371118:0.597937:0.367308:0.597937:0.000000 es la función denotada “ ” y definida como: :@0.371044:0.614884:0.687044:0.614882:0.687044:0.599169:0.371044:0.599172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.546464:0.614327:0.552593:0.614327:0.552593:0.600611:0.546464:0.600611:0.000000 R R:@0.330130:0.638922:0.375007:0.638922:0.375007:0.625438:0.330130:0.625438:0.000000:0.000000:0.000000 :@0.344024:0.639663:0.362843:0.639663:0.362843:0.623950:0.344024:0.623950:0.000000:0.000000:0.000000 .:@0.375007:0.639821:0.418017:0.639821:0.418017:0.623394:0.375007:0.623394:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.379220:0.639108:0.396563:0.639108:0.396563:0.622892:0.379220:0.622892:0.000000 R:@0.400774:0.638922:0.414669:0.638922:0.414669:0.625438:0.400774:0.625438:0.000000 (:@0.330130:0.664613:0.335230:0.664613:0.335230:0.648186:0.330130:0.648186:0.000000 x, y:@0.335230:0.664613:0.357783:0.664613:0.357783:0.648476:0.335230:0.648476:0.000000:0.000000:0.000000:0.000000 ) :@0.357783:0.664613:0.388651:0.664619:0.388651:0.648193:0.357783:0.648186:0.000000:0.000000:0.000000:0.000000 →:@0.367098:0.663907:0.384441:0.663907:0.384441:0.647691:0.367098:0.647691:0.000000 x y:@0.388651:0.664619:0.415267:0.664619:0.415267:0.648482:0.388651:0.648482:0.000000:0.000000:0.000000 :@0.396445:0.664462:0.409184:0.664462:0.409184:0.648749:0.396445:0.648749:0.000000:0.000000:0.000000 ?:@0.398745:0.664039:0.405154:0.664039:0.405154:0.649700:0.398745:0.649700:0.000000 .:@0.415267:0.664619:0.418615:0.664619:0.418615:0.648193:0.415267:0.648193:0.000000 • : :@0.294126:0.652426:0.314698:0.652426:0.314698:0.635999:0.294126:0.635999:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.310484:0.652426:0.314698:0.652426:0.314698:0.635999:0.310484:0.635999:0.000000 De la definición de la operación producto, tenemos , :@0.293660:0.693811:0.677210:0.693811:0.677210:0.678098:0.293660:0.678098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.638031:0.693811:0.658095:0.693811:0.658095:0.678375:0.638031:0.678375:0.000000:0.000000:0.000000 R:@0.675398:0.692951:0.688688:0.692951:0.688688:0.680053:0.675398:0.680053:0.000000 ⇒ :@0.688596:0.693256:0.709628:0.693256:0.709628:0.677040:0.688596:0.677040:0.000000:0.000000 x y:@0.709005:0.693811:0.733056:0.693811:0.733056:0.678375:0.709005:0.678375:0.000000:0.000000:0.000000 . Entonces, se dice que :@0.715750:0.693811:0.931066:0.693811:0.931066:0.678098:0.715750:0.678098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.717969:0.693256:0.724099:0.693256:0.724099:0.679540:0.717969:0.679540:0.000000 R:@0.750347:0.692951:0.763637:0.692951:0.763637:0.680053:0.750347:0.680053:0.000000 la multiplicación de números reales es cerrada.:@0.293663:0.710453:0.631713:0.710453:0.631713:0.694740:0.293663:0.694740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.3 Propiedades en número reales :@0.293663:0.737814:0.564202:0.737814:0.564202:0.720868:0.293663:0.720868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.564048:0.736955:0.577338:0.736955:0.577338:0.724057:0.564048:0.724057:0.000000 Adición:@0.293663:0.765176:0.351827:0.765176:0.351827:0.748507:0.293663:0.748507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Conmutativa: para todo , :@0.293658:0.792542:0.533774:0.792542:0.533774:0.775873:0.293658:0.775873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.507526:0.792542:0.529946:0.792542:0.529946:0.777107:0.507526:0.777107:0.000000:0.000000:0.000000 ,:@0.565835:0.792542:0.569038:0.792542:0.569038:0.776829:0.565835:0.776829:0.000000 :@0.568405:0.792542:0.663184:0.792542:0.663184:0.775873:0.568405:0.775873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.572234:0.792542:0.579689:0.792542:0.579689:0.777107:0.572234:0.777107:0.000000 1 5 1:@0.583444:0.791987:0.659374:0.791987:0.659374:0.778272:0.583444:0.778272:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.602514:0.792542:0.609987:0.792542:0.609987:0.777107:0.602514:0.777107:0.000000 y:@0.632812:0.792542:0.640285:0.792542:0.640285:0.777107:0.632812:0.777107:0.000000 x:@0.663110:0.792542:0.670565:0.792542:0.670565:0.777107:0.663110:0.777107:0.000000 .:@0.670492:0.792542:0.673695:0.792542:0.673695:0.776829:0.670492:0.776829:0.000000 2. Asociativa: para todo , , :@0.293658:0.817403:0.527221:0.817403:0.527221:0.800733:0.293658:0.800733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404758:0.817403:0.408568:0.817403:0.408568:0.800456:0.404758:0.800456:0.000000 x y z:@0.486247:0.817403:0.523393:0.817403:0.523393:0.801967:0.486247:0.801967:0.000000:0.000000:0.000000:0.000000:0.000000 ,:@0.559268:0.817403:0.562471:0.817403:0.562471:0.801690:0.559268:0.801690:0.000000 :@0.562391:0.817403:0.736726:0.817403:0.736726:0.800733:0.562391:0.800733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.566220:0.817403:0.573675:0.817403:0.573675:0.801967:0.566220:0.801967:0.000000 1:@0.577430:0.816848:0.592763:0.816848:0.592763:0.803132:0.577430:0.803132:0.000000 (:@0.596500:0.817403:0.601378:0.817403:0.601378:0.801690:0.596500:0.801690:0.000000 y:@0.601304:0.817403:0.608777:0.817403:0.608777:0.801967:0.601304:0.801967:0.000000 1:@0.612532:0.816848:0.627866:0.816848:0.627866:0.803132:0.612532:0.803132:0.000000 z:@0.631602:0.817403:0.638836:0.817403:0.638836:0.801967:0.631602:0.801967:0.000000 ):@0.638763:0.817403:0.643641:0.817403:0.643641:0.801690:0.638763:0.801690:0.000000 5:@0.647396:0.816848:0.662729:0.816848:0.662729:0.803132:0.647396:0.803132:0.000000 (:@0.666466:0.817403:0.671344:0.817403:0.671344:0.801690:0.666466:0.801690:0.000000 x:@0.671270:0.817403:0.678725:0.817403:0.678725:0.801967:0.671270:0.801967:0.000000 1:@0.682480:0.816848:0.697813:0.816848:0.697813:0.803132:0.682480:0.803132:0.000000 y:@0.701550:0.817403:0.709023:0.817403:0.709023:0.801967:0.701550:0.801967:0.000000 ):@0.708950:0.817403:0.713827:0.817403:0.713827:0.801690:0.708950:0.801690:0.000000 1:@0.717583:0.816848:0.732916:0.816848:0.732916:0.803132:0.717583:0.803132:0.000000 z.:@0.736652:0.817403:0.747145:0.817403:0.747145:0.801967:0.736652:0.801967:0.000000:0.000000 3. Existencia de elemento neutro::@0.293658:0.842265:0.587884:0.842265:0.587884:0.825595:0.293658:0.825595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.588168:0.842265:0.591978:0.842265:0.591978:0.825318:0.588168:0.825318:0.000000 existe 0 :@0.597371:0.842265:0.665173:0.842265:0.665173:0.826552:0.597371:0.826552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tal que para todo :@0.704249:0.842265:0.867418:0.842265:0.867418:0.826552:0.704249:0.826552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.873268:0.842265:0.880723:0.842265:0.880723:0.826829:0.873268:0.826829:0.000000 :@0.880980:0.842265:0.884883:0.842265:0.884883:0.825595:0.880980:0.825595:0.000000 ,:@0.923709:0.842265:0.926911:0.842265:0.926911:0.826552:0.923709:0.826552:0.000000 :@0.926911:0.842265:0.930814:0.842265:0.930814:0.825595:0.926911:0.825595:0.000000:0.000000:0.000000 x:@0.323779:0.858906:0.331234:0.858906:0.331234:0.843471:0.323779:0.843471:0.000000 :@0.331161:0.858906:0.335063:0.858906:0.335063:0.842237:0.331161:0.842237:0.000000 1 5 1 5:@0.334989:0.858352:0.444697:0.858352:0.444697:0.844636:0.334989:0.844636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0 0 :@0.350231:0.858906:0.399176:0.858906:0.399176:0.843194:0.350231:0.843194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.414325:0.858906:0.448507:0.858906:0.448507:0.842237:0.414325:0.842237:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.418153:0.858906:0.425608:0.858906:0.425608:0.843471:0.418153:0.843471:0.000000 x:@0.448433:0.858906:0.455888:0.858906:0.455888:0.843471:0.448433:0.843471:0.000000 .:@0.455815:0.858906:0.459018:0.858906:0.459018:0.843194:0.455815:0.843194:0.000000 4. Existencia de opuestos aditivos::@0.293658:0.883768:0.561054:0.883768:0.561054:0.867099:0.293658:0.867099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para cada:@0.560907:0.883768:0.634407:0.883768:0.634407:0.868056:0.560907:0.868056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.634260:0.883768:0.648930:0.883768:0.648930:0.867099:0.634260:0.867099:0.000000:0.000000:0.000000 x:@0.637665:0.883768:0.645120:0.883768:0.645120:0.868333:0.637665:0.868333:0.000000 , existe :@0.680505:0.883768:0.732521:0.883768:0.732521:0.868056:0.680505:0.868056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.731974:0.883214:0.747307:0.883214:0.747307:0.869498:0.731974:0.869498:0.000000 x:@0.747178:0.883768:0.754633:0.883768:0.754633:0.868333:0.747178:0.868333:0.000000 :@0.754541:0.883768:0.758443:0.883768:0.758443:0.867099:0.754541:0.867099:0.000000 tal que :@0.790023:0.883768:0.847049:0.883768:0.847049:0.868056:0.790023:0.868056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.846499:0.883768:0.853954:0.883768:0.853954:0.868333:0.846499:0.868333:0.000000 :@0.853861:0.883768:0.857764:0.883768:0.857764:0.867099:0.853861:0.867099:0.000000 1 2 5:@0.857267:0.883214:0.926938:0.883214:0.926938:0.869498:0.857267:0.869498:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.872471:0.883768:0.880865:0.883768:0.880865:0.868056:0.872471:0.868056:0.000000:0.000000 x:@0.895959:0.883768:0.903414:0.883768:0.903414:0.868333:0.895959:0.868333:0.000000 ) :@0.903322:0.883768:0.912120:0.883768:0.912120:0.868056:0.903322:0.868056:0.000000:0.000000 :@0.926938:0.883768:0.930841:0.883768:0.930841:0.867099:0.926938:0.867099:0.000000 2 1 5:@0.323806:0.899855:0.395871:0.899855:0.395871:0.886140:0.323806:0.886140:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.339047:0.900410:0.346502:0.900410:0.346502:0.884975:0.339047:0.884975:0.000000 :@0.346429:0.900410:0.380611:0.900410:0.380611:0.883741:0.346429:0.883741:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.369327:0.900410:0.376782:0.900410:0.376782:0.884975:0.369327:0.884975:0.000000 0.:@0.395779:0.900410:0.411848:0.900410:0.411848:0.884698:0.395779:0.884698:0.000000:0.000000:0.000000 Las propiedades, de la 1 a la 4, dan la :@0.293692:0.925276:0.571098:0.925276:0.571098:0.909563:0.293692:0.909563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estructura:@0.571476:0.925276:0.649916:0.925276:0.649916:0.908606:0.571476:0.908606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 algebraica que denominamos :@0.649891:0.925276:0.879613:0.925276:0.879613:0.909563:0.649891:0.909563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 grupo :@0.879981:0.925276:0.930872:0.925276:0.930872:0.908606:0.879981:0.908606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conmutativo de la adición de números reales:@0.293692:0.941918:0.633819:0.941918:0.633819:0.925248:0.293692:0.925248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , que se escribe ( , ).:@0.633563:0.941918:0.796799:0.941918:0.796799:0.926205:0.633563:0.926205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.753284:0.941058:0.766574:0.941058:0.766574:0.928160:0.753284:0.928160:0.000000 1:@0.773551:0.941363:0.788884:0.941363:0.788884:0.927647:0.773551:0.927647:0.000000 1:@0.294152:0.514417:0.309485:0.514417:0.309485:0.500701:0.294152:0.500701:0.000000 : :@0.309393:0.514971:0.316627:0.514971:0.316627:0.499259:0.309393:0.499259:0.000000:0.000000 Por las limitaciones de las :@0.082576:0.180962:0.253154:0.180962:0.253154:0.166678:0.082576:0.166678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calculadoras de bolsillo, :@0.082576:0.196091:0.242093:0.196091:0.242093:0.181807:0.082576:0.181807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los datos mostrados se :@0.082576:0.211220:0.236588:0.211220:0.236588:0.196936:0.082576:0.196936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 presentan hasta con 9 :@0.082576:0.226349:0.232136:0.226349:0.232136:0.212065:0.082576:0.212065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cifras (a veces 10 o 12 :@0.082576:0.241478:0.228189:0.241478:0.228189:0.227194:0.082576:0.227194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cifras) después del punto :@0.082576:0.256607:0.251949:0.256607:0.251949:0.242323:0.082576:0.242323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decimal.:@0.082576:0.271736:0.137849:0.271736:0.137849:0.257452:0.082576:0.257452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sin embargo, mediante :@0.082576:0.286865:0.240666:0.286865:0.240666:0.272581:0.082576:0.272581:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el uso de programas :@0.082576:0.301994:0.220868:0.301994:0.220868:0.287710:0.082576:0.287710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 específcos (Matlab, :@0.082576:0.317123:0.211442:0.317123:0.211442:0.302839:0.082576:0.302839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Mathematica, Derive, :@0.082576:0.332252:0.225450:0.332252:0.225450:0.317967:0.082576:0.317967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 GeoGebra, entre otros) :@0.082576:0.347381:0.236534:0.347381:0.236534:0.333096:0.082576:0.333096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se pueden obtener :@0.082576:0.362510:0.212625:0.362510:0.212625:0.348225:0.082576:0.348225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aproximaciones con :@0.082576:0.377639:0.219614:0.377639:0.219614:0.363354:0.082576:0.363354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un número grande de :@0.082576:0.392767:0.232113:0.392767:0.232113:0.378483:0.082576:0.378483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cifras decimales. Así, por :@0.082576:0.407896:0.245165:0.407896:0.245165:0.393612:0.082576:0.393612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ejemplo, se aproxima :@0.082576:0.423025:0.246951:0.423025:0.246951:0.408741:0.082576:0.408741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.152396:0.423504:0.158324:0.423504:0.158324:0.411939:0.152396:0.411939:0.000000 con 19 cifras después del :@0.082576:0.438154:0.251789:0.438154:0.251789:0.423870:0.082576:0.423870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 punto decimal.:@0.082576:0.453283:0.182179:0.453283:0.182179:0.438999:0.082576:0.438999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 1,414 213 562 373 095 048 8. :@0.089463:0.468995:0.262922:0.468995:0.262922:0.457567:0.089463:0.457567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De la misma manera, :@0.082576:0.593643:0.224782:0.593643:0.224782:0.579359:0.082576:0.579359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 al utilizar este tipo de :@0.082576:0.608772:0.225945:0.608772:0.225945:0.594488:0.082576:0.594488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 programas especializados, :@0.082576:0.623901:0.258849:0.623901:0.258849:0.609617:0.082576:0.609617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 podemos obtener valores :@0.082576:0.639030:0.256360:0.639030:0.256360:0.624746:0.082576:0.624746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aproximados de con 32 :@0.082576:0.654159:0.255939:0.654159:0.255939:0.639875:0.082576:0.639875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.192601:0.653655:0.203762:0.653655:0.203762:0.641186:0.192601:0.641186:0.000000 cifras, como se muestra a :@0.082576:0.669288:0.251715:0.669288:0.251715:0.655004:0.082576:0.655004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 continuación::@0.082576:0.684417:0.172972:0.684417:0.172972:0.670133:0.082576:0.670133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.082576:0.699042:0.093737:0.699042:0.093737:0.686573:0.082576:0.686573:0.000000 = 3,1415926 535 897 9:@0.093654:0.699546:0.245949:0.699546:0.245949:0.685262:0.093654:0.685262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 32 384 626 433 832 795 0.:@0.082576:0.714675:0.252860:0.714675:0.252860:0.700391:0.082576:0.700391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.080204:0.136836:0.188764:0.136836:0.188764:0.119889:0.080204:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 digital:@0.080204:0.153478:0.130896:0.153478:0.130896:0.136531:0.080204:0.136531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Estructura:@0.085307:0.868913:0.155691:0.867524:0.155165:0.852375:0.084781:0.853764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Disposición :@0.155591:0.867526:0.242277:0.865816:0.241780:0.851537:0.155095:0.853247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 o modo de estar :@0.085825:0.884037:0.198306:0.881818:0.197809:0.867538:0.085329:0.869758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 relacionada con las :@0.086351:0.899161:0.215954:0.896604:0.215458:0.882324:0.085855:0.884881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 distintas partes de un :@0.086877:0.914285:0.232265:0.911416:0.231768:0.897137:0.086380:0.900005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conjunto.:@0.087402:0.929408:0.150187:0.928170:0.149690:0.913890:0.086906:0.915129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Glosario:@0.137493:0.838688:0.197112:0.838688:0.197112:0.823282:0.137493:0.823282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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