15:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento numérico y variacional :@0.603816:0.043660:0.930949:0.043660:0.930949:0.024915:0.603816:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.1 Representación geométrica:@0.073089:0.136836:0.317585:0.136836:0.317585:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los números reales se representan sobre una recta numérica, de manera que a cada :@0.073089:0.164199:0.710068:0.164199:0.710068:0.147766:0.073089:0.147766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
punto le corresponde un número real diferente y viceversa. Esto es llamado una :@0.073089:0.180841:0.710313:0.180841:0.710313:0.164407:0.073089:0.164407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
correspondencia uno a uno. El origen O tiene asignado el número cero (0). Hacia la :@0.073089:0.197483:0.710405:0.197483:0.710405:0.181049:0.073089:0.181049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
derecha están los números naturales o enteros positivos y hacia la izquierda se ubican los :@0.073089:0.214125:0.710122:0.214125:0.710122:0.197691:0.073089:0.197691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números enteros negativos. Para ubicar un número decimal, primero se ubica la parte :@0.073089:0.230767:0.710400:0.230767:0.710400:0.214333:0.073089:0.214333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entera y luego la parte correspondiente a la cifra decimal. En el caso de un número :@0.073089:0.247409:0.710880:0.247409:0.710880:0.230975:0.073089:0.230975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fraccionario se simplifica y si es impropio, se expresa como un número mixto ubicando :@0.073089:0.264050:0.710573:0.264050:0.710573:0.247617:0.073089:0.247617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
primero la parte entera y luego la fracción decimal. Algunos números irracionales como :@0.073089:0.280692:0.710808:0.280692:0.710808:0.264258:0.073089:0.264258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2  o  3 se pueden construir con el apoyo de triángulos rectángulos y un cormpás. Esta :@0.084855:0.297495:0.710434:0.298897:0.710434:0.282464:0.084855:0.281062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta numérica es también llamada recta real. :@0.073089:0.315539:0.405955:0.315539:0.405955:0.299105:0.073089:0.299105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 1. Recta numérica o recta real:@0.247350:0.353621:0.532151:0.353621:0.532151:0.336674:0.247350:0.336674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
_:@0.110389:0.384392:0.117324:0.384392:0.117324:0.371833:0.110389:0.371833:0.000000
4.9:@0.117324:0.389617:0.134424:0.389617:0.134424:0.377057:0.117324:0.377057:0.000000:0.000000:0.000000
_:@0.148349:0.384392:0.155283:0.384392:0.155283:0.371833:0.148349:0.371833:0.000000
4.7:@0.155283:0.389617:0.172384:0.389617:0.172384:0.377057:0.155283:0.377057:0.000000:0.000000:0.000000
_:@0.180400:0.416011:0.187335:0.416011:0.187335:0.403451:0.180400:0.403451:0.000000
4:@0.187335:0.421236:0.194450:0.421236:0.194450:0.408676:0.187335:0.408676:0.000000
_:@0.228137:0.416011:0.235072:0.416011:0.235072:0.403451:0.228137:0.403451:0.000000
3:@0.235072:0.421236:0.242187:0.421236:0.242187:0.408676:0.235072:0.408676:0.000000
_:@0.282240:0.416011:0.289175:0.416011:0.289175:0.403451:0.282240:0.403451:0.000000
2:@0.289175:0.421236:0.296290:0.421236:0.296290:0.408676:0.289175:0.408676:0.000000
_:@0.332932:0.416011:0.339866:0.416011:0.339866:0.403451:0.332932:0.403451:0.000000
1:@0.339866:0.421236:0.346981:0.421236:0.346981:0.408676:0.339866:0.408676:0.000000
1:@0.440805:0.421236:0.447920:0.421236:0.447920:0.408676:0.440805:0.408676:0.000000
2:@0.491732:0.421236:0.498847:0.421236:0.498847:0.408676:0.491732:0.408676:0.000000
3:@0.546057:0.421236:0.553172:0.421236:0.553172:0.408676:0.546057:0.408676:0.000000
4:@0.598343:0.421236:0.605458:0.421236:0.605458:0.408676:0.598343:0.408676:0.000000
4.3:@0.597220:0.434078:0.614321:0.434078:0.614321:0.421518:0.597220:0.421518:0.000000:0.000000:0.000000
4.5:@0.629507:0.434078:0.646608:0.434078:0.646608:0.421518:0.629507:0.421518:0.000000:0.000000:0.000000
4.9999:@0.652932:0.389889:0.691377:0.389889:0.691377:0.377329:0.652932:0.377329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.4:@0.620548:0.389889:0.637648:0.389889:0.637648:0.377329:0.620548:0.377329:0.000000:0.000000:0.000000
4.2:@0.594834:0.389889:0.611935:0.389889:0.611935:0.377329:0.594834:0.377329:0.000000:0.000000:0.000000
5:@0.510539:0.400338:0.517653:0.400338:0.517653:0.387778:0.510539:0.387778:0.000000
3:@0.495657:0.391519:0.502772:0.391519:0.502772:0.378959:0.495657:0.378959:0.000000
2:@0.466768:0.400003:0.473883:0.400003:0.473883:0.387443:0.466768:0.387443:0.000000
5:@0.648591:0.421225:0.655706:0.421225:0.655706:0.408665:0.648591:0.408665:0.000000
_:@0.410834:0.426795:0.417769:0.426795:0.417769:0.414235:0.410834:0.414235:0.000000
0:@0.388241:0.421403:0.395356:0.421403:0.395356:0.408843:0.388241:0.408843:0.000000
0.3:@0.401431:0.436993:0.418532:0.436993:0.418532:0.424433:0.401431:0.424433:0.000000:0.000000:0.000000
_:@0.137752:0.427829:0.144687:0.427829:0.144687:0.415269:0.137752:0.415269:0.000000
4.85:@0.144687:0.433053:0.168902:0.433053:0.168902:0.420494:0.144687:0.420494:0.000000:0.000000:0.000000:0.000000
_:@0.118571:0.416011:0.125506:0.416011:0.125506:0.403451:0.118571:0.403451:0.000000
5:@0.125506:0.421235:0.132621:0.421235:0.132621:0.408676:0.125506:0.408676:0.000000
2:@0.323733:0.400013:0.330847:0.400013:0.330847:0.387453:0.323733:0.387453:0.000000
2.63:@0.248438:0.400013:0.272653:0.400013:0.272653:0.387453:0.248438:0.387453:0.000000:0.000000:0.000000:0.000000
2:@0.415973:0.399014:0.423088:0.399014:0.423088:0.386455:0.415973:0.386455:0.000000
1 _:@0.415973:0.386361:0.423102:0.388158:0.423102:0.375598:0.415973:0.373801:0.000000:0.000000:0.000000
1:@0.400661:0.378095:0.407776:0.378095:0.407776:0.365536:0.400661:0.365536:0.000000
1:@0.384768:0.378095:0.391882:0.378095:0.391882:0.365536:0.384768:0.365536:0.000000
1:@0.368305:0.378095:0.375420:0.378095:0.375420:0.365536:0.368305:0.365536:0.000000
4:@0.401535:0.391407:0.408650:0.391407:0.408650:0.378848:0.401535:0.378848:0.000000
8:@0.385350:0.391407:0.392465:0.391407:0.392465:0.378848:0.385350:0.378848:0.000000
16:@0.364450:0.391407:0.378679:0.391407:0.378679:0.378848:0.364450:0.378848:0.000000:0.000000
_:@0.354325:0.380541:0.361260:0.380541:0.361260:0.367981:0.354325:0.367981:0.000000
_:@0.239323:0.395995:0.246258:0.395995:0.246258:0.383435:0.239323:0.383435:0.000000
_:@0.305492:0.395995:0.312427:0.395995:0.312427:0.383435:0.305492:0.383435:0.000000
3.1725:@0.209824:0.389349:0.248269:0.389349:0.248269:0.376789:0.209824:0.376789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
_:@0.202640:0.385326:0.209574:0.385326:0.209574:0.372766:0.202640:0.372766:0.000000
∏:@0.551410:0.400390:0.559940:0.400390:0.559940:0.387830:0.551410:0.387830:0.000000
Fuente: Swokowski (2011).:@0.303170:0.465263:0.476371:0.465263:0.476371:0.450323:0.303170:0.450323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.2 Operaciones y propiedades en    :@0.073089:0.503663:0.364347:0.503663:0.364347:0.486716:0.073089:0.486716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.343436:0.504245:0.356726:0.504245:0.356726:0.486591:0.343436:0.486591:0.000000
Adición:@0.073089:0.534395:0.133408:0.534395:0.133408:0.517448:0.073089:0.517448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sea:@0.133317:0.534395:0.165983:0.534395:0.165983:0.517961:0.133317:0.517961:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.165898:0.540705:0.169929:0.540705:0.169929:0.524271:0.165898:0.524271:0.000000
+:@0.275733:0.534366:0.286704:0.534366:0.286704:0.518653:0.275733:0.518653:0.000000
. En este caso, se dice “la suma de números reales es :@0.334529:0.534400:0.710578:0.534400:0.710578:0.517966:0.334529:0.517966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cerrada o cumple con la propiedad clausurativa”.:@0.073089:0.551041:0.423572:0.551041:0.423572:0.534608:0.073089:0.534608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.3 Propiedades de la adición en :@0.073089:0.589123:0.330343:0.589123:0.330343:0.572177:0.073089:0.572177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.330183:0.589706:0.343473:0.589706:0.343473:0.572052:0.330183:0.572052:0.000000
 :@0.343473:0.591647:0.347283:0.591647:0.347283:0.574701:0.343473:0.574701:0.000000
La adición de números reales cumple con las siguientes propiedades::@0.073089:0.616485:0.574740:0.616485:0.574740:0.600052:0.073089:0.600052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedad:@0.149474:0.653536:0.231436:0.653536:0.231436:0.636589:0.149474:0.636589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Notación:@0.470571:0.653536:0.542580:0.653536:0.542580:0.636589:0.470571:0.636589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conmutativa:@0.080410:0.685697:0.179642:0.685697:0.179642:0.669027:0.080410:0.669027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo  ,   :@0.314716:0.687291:0.414981:0.687291:0.414981:0.670858:0.314716:0.670858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.388787:0.687291:0.410949:0.687291:0.410949:0.670885:0.388787:0.670885:0.000000:0.000000:0.000000
∈ ℝ:@0.414981:0.687874:0.448206:0.687874:0.448206:0.670220:0.414981:0.670220:0.000000:0.000000:0.000000
,   +   =   +  . :@0.448206:0.687291:0.549630:0.687291:0.549630:0.670858:0.448206:0.670858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.455440:0.687291:0.462895:0.687291:0.462895:0.670885:0.455440:0.670885:0.000000
y:@0.481928:0.687291:0.489401:0.687291:0.489401:0.670885:0.481928:0.670885:0.000000
y:@0.508434:0.687291:0.515908:0.687291:0.515908:0.670885:0.508434:0.670885:0.000000
x:@0.534941:0.687291:0.542396:0.687291:0.542396:0.670885:0.534941:0.670885:0.000000
Asociativa:@0.080410:0.719050:0.158365:0.719050:0.158365:0.702380:0.080410:0.702380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo  , ,   :@0.314716:0.720658:0.428731:0.720658:0.428731:0.704224:0.314716:0.704224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x  y z:@0.388787:0.720658:0.424700:0.720658:0.424700:0.704252:0.388787:0.704252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℝ:@0.428731:0.721241:0.461956:0.721241:0.461956:0.703586:0.428731:0.703586:0.000000:0.000000:0.000000
,   + (  +  ) = ( +  ) + :@0.461956:0.720658:0.623553:0.720658:0.623553:0.704224:0.461956:0.704224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.469190:0.720658:0.476645:0.720658:0.476645:0.704252:0.469190:0.704252:0.000000
y  z:@0.504587:0.720658:0.537610:0.720658:0.537610:0.704252:0.504587:0.704252:0.000000:0.000000:0.000000:0.000000
x  y:@0.566399:0.720658:0.599642:0.720658:0.599642:0.704252:0.566399:0.704252:0.000000:0.000000:0.000000:0.000000
z.:@0.623553:0.720658:0.634119:0.720658:0.634119:0.704252:0.623553:0.704252:0.000000:0.000000
Existencia del elemento :@0.080410:0.750835:0.265678:0.750835:0.265678:0.734166:0.080410:0.734166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
neutro:@0.080410:0.767477:0.132024:0.767477:0.132024:0.750808:0.080410:0.750808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para todo :@0.314716:0.752666:0.388787:0.752666:0.388787:0.736232:0.314716:0.736232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.388787:0.752666:0.399555:0.752666:0.399555:0.736260:0.388787:0.736260:0.000000:0.000000
∈ ℝ:@0.399555:0.753248:0.432780:0.753248:0.432780:0.735594:0.399555:0.735594:0.000000:0.000000:0.000000
, existe 0 :@0.432780:0.752666:0.499100:0.752666:0.499100:0.736232:0.432780:0.736232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈ ℝ:@0.499100:0.753248:0.532325:0.753248:0.532325:0.735594:0.499100:0.735594:0.000000:0.000000:0.000000
 tal que :@0.532325:0.752666:0.591044:0.752666:0.591044:0.736232:0.532325:0.736232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.314716:0.768850:0.322171:0.768850:0.322171:0.752444:0.314716:0.752444:0.000000
 + 0 = 0 +   =  .:@0.322171:0.768850:0.434382:0.768850:0.434382:0.752416:0.322171:0.752416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.397236:0.768850:0.404691:0.768850:0.404691:0.752444:0.397236:0.752444:0.000000
x:@0.423724:0.768850:0.431179:0.768850:0.431179:0.752444:0.423724:0.752444:0.000000
Existencia de opuestos :@0.080410:0.797890:0.258351:0.797890:0.258351:0.781221:0.080410:0.781221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aditivos:@0.080410:0.814532:0.140436:0.814532:0.140436:0.797862:0.080410:0.797862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para cada :@0.314716:0.799721:0.388548:0.799721:0.388548:0.783287:0.314716:0.783287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.388548:0.799721:0.399316:0.799721:0.399316:0.783315:0.388548:0.783315:0.000000:0.000000
∈ ℝ:@0.399316:0.800303:0.432541:0.800303:0.432541:0.782649:0.399316:0.782649:0.000000:0.000000:0.000000
, existe −:@0.432541:0.799721:0.496817:0.799721:0.496817:0.783287:0.432541:0.783287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.496817:0.799721:0.507586:0.799721:0.507586:0.783315:0.496817:0.783315:0.000000:0.000000
∈ ℝ:@0.507586:0.800303:0.540811:0.800303:0.540811:0.782649:0.507586:0.782649:0.000000:0.000000:0.000000
, tal que:@0.540811:0.799721:0.598702:0.799721:0.598702:0.783287:0.540811:0.783287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.598702:0.799721:0.602015:0.799721:0.602015:0.783315:0.598702:0.783315:0.000000
x:@0.314716:0.815905:0.322171:0.815905:0.322171:0.799499:0.314716:0.799499:0.000000
 + (− ) = −  +   = 0.:@0.322171:0.815905:0.464551:0.815905:0.464551:0.799471:0.322171:0.799471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.357053:0.815905:0.364508:0.815905:0.364508:0.799499:0.357053:0.799499:0.000000
x:@0.399390:0.815905:0.406845:0.815905:0.406845:0.799499:0.399390:0.799499:0.000000
x:@0.425878:0.815905:0.433333:0.815905:0.433333:0.799499:0.425878:0.799499:0.000000
Interdisciplinariedad :@0.744486:0.166169:0.896871:0.166169:0.896871:0.150762:0.744486:0.150762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemáticas :@0.744486:0.181298:0.832676:0.181298:0.832676:0.166358:0.744486:0.166358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e historia:@0.744486:0.196427:0.804481:0.196427:0.804481:0.181487:0.744486:0.181487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El cero es fascinante :@0.744486:0.228494:0.881936:0.228494:0.881936:0.213554:0.744486:0.213554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por dos funciones :@0.744486:0.243623:0.868233:0.243623:0.868233:0.228683:0.744486:0.228683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
básicas: representa la :@0.744486:0.258752:0.888479:0.258752:0.888479:0.243812:0.744486:0.243812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nada y actúa como un :@0.744486:0.273880:0.897164:0.273880:0.897164:0.258941:0.744486:0.258941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elemento posicional. :@0.744486:0.289009:0.886939:0.289009:0.886939:0.274070:0.744486:0.274070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En numeración, el :@0.744486:0.304138:0.867864:0.304138:0.867864:0.289199:0.744486:0.289199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cero posicional ayuda :@0.744486:0.319267:0.893014:0.319267:0.893014:0.304327:0.744486:0.304327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a diferenciar números :@0.744486:0.334396:0.892830:0.334396:0.892830:0.319456:0.744486:0.319456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como 2024 de 224. :@0.744486:0.349525:0.875411:0.349525:0.875411:0.334585:0.744486:0.334585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Este concepto fue :@0.744486:0.364654:0.868214:0.364654:0.868214:0.349714:0.744486:0.349714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inicialmente desarrollado :@0.744486:0.379783:0.916324:0.379783:0.916324:0.364843:0.744486:0.364843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por los babilonios y los :@0.744486:0.394912:0.900261:0.394912:0.900261:0.379972:0.744486:0.379972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mayas, y luego llegó a :@0.744486:0.410041:0.894672:0.410041:0.894672:0.395101:0.744486:0.395101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la India. En la India, el :@0.744486:0.425170:0.888914:0.425170:0.888914:0.410230:0.744486:0.410230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cero evolucionó de ser :@0.744486:0.440299:0.899592:0.440299:0.899592:0.425359:0.744486:0.425359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un mero marcador de :@0.744486:0.455428:0.893750:0.455428:0.893750:0.440488:0.744486:0.440488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
posición a convertirse en :@0.744486:0.470557:0.914600:0.470557:0.914600:0.455617:0.744486:0.455617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un número con entidad :@0.744486:0.485686:0.907221:0.485686:0.907221:0.470746:0.744486:0.470746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propia, integrándose en :@0.744486:0.500815:0.907187:0.500815:0.907187:0.485875:0.744486:0.485875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la aritmética.:@0.744486:0.515944:0.829075:0.515944:0.829075:0.501004:0.744486:0.501004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El nombre \cero\ :@0.744486:0.538221:0.859596:0.538221:0.859596:0.523281:0.744486:0.523281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proviene del término :@0.744486:0.553350:0.888629:0.553350:0.888629:0.538410:0.744486:0.538410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
árabe :@0.744486:0.568479:0.785634:0.568479:0.785634:0.553539:0.744486:0.553539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sifr:@0.785634:0.568479:0.803941:0.568479:0.803941:0.553564:0.785634:0.553564:0.000000:0.000000:0.000000:0.000000
 que significa :@0.803941:0.568479:0.895340:0.568479:0.895340:0.553539:0.803941:0.553539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
\vacío\. Este número :@0.744486:0.583608:0.882706:0.583608:0.882706:0.568668:0.744486:0.568668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llegó a Europa gracias a :@0.744486:0.598737:0.904610:0.598737:0.904610:0.583797:0.744486:0.583797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los matemáticos árabes, :@0.744486:0.613866:0.907688:0.613866:0.907688:0.598926:0.744486:0.598926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
quienes transmitieron el :@0.744486:0.628995:0.909563:0.628995:0.909563:0.614055:0.744486:0.614055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concepto del cero al Viejo :@0.744486:0.644123:0.919955:0.644123:0.919955:0.629184:0.744486:0.629184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Continente.:@0.744486:0.659252:0.822447:0.659252:0.822447:0.644313:0.744486:0.644313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Puedes decir si el cero es :@0.744486:0.884245:0.919518:0.884245:0.919518:0.869305:0.744486:0.869305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un número par o impar?:@0.744486:0.899374:0.906351:0.899374:0.906351:0.884434:0.744486:0.884434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 1 (Ev. 3) Construye representaciones geométricas y numéricas de los números reales (con decimales, raíces, razones, y otros símbolos) :@0.086324:0.965506:0.816233:0.965506:0.816233:0.953554:0.086324:0.953554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y realiza conversiones entre ellas.:@0.086324:0.977609:0.259205:0.977609:0.259205:0.965657:0.086324:0.965657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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