197:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000
Si una función   de   en   es tal que :@0.108233:0.096194:0.366885:0.096194:0.366885:0.079697:0.108233:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.214344:0.096310:0.218640:0.096310:0.218640:0.079841:0.214344:0.079841:0.000000
A:@0.244743:0.096310:0.256013:0.096310:0.256013:0.079841:0.244743:0.079841:0.000000
B:@0.281809:0.096310:0.290999:0.096310:0.290999:0.079841:0.281809:0.079841:0.000000
Rec f:@0.366865:0.096310:0.401007:0.096310:0.401007:0.079841:0.366865:0.079841:0.000000:0.000000:0.000000:0.000000:0.000000
( ) es un subconjunto propio :@0.390758:0.096194:0.599902:0.096194:0.599902:0.079697:0.390758:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de  ,  no es sobreyectiva.:@0.108233:0.113545:0.288841:0.113545:0.288841:0.097047:0.108233:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B f :@0.130234:0.113661:0.154759:0.113661:0.154759:0.097192:0.130234:0.097192:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.108233:0.148622:0.238888:0.148622:0.238888:0.131836:0.108233:0.131836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108233:0.165814:0.120505:0.165814:0.120505:0.149100:0.108233:0.149100:0.000000:0.000000
  Sean   = { ,  ,  ,  },   = {1, 2, 3, 4}  y   la función de   en   definida :@0.120506:0.165597:0.599871:0.165597:0.599871:0.149100:0.120506:0.149100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.169439:0.165713:0.180709:0.165713:0.180709:0.149244:0.169439:0.149244:0.000000
a b c d B:@0.205020:0.165713:0.280946:0.165713:0.280946:0.149244:0.205020:0.149244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.384137:0.165713:0.388433:0.165713:0.388433:0.149244:0.384137:0.149244:0.000000
A:@0.488242:0.165713:0.499512:0.165713:0.499512:0.149244:0.488242:0.149244:0.000000
B:@0.524690:0.165713:0.533880:0.165713:0.533880:0.149244:0.524690:0.149244:0.000000
como  ( ) = 3,     ( ) = 2,     ( ) = 1,     ( ) = 4. :@0.131929:0.182948:0.452484:0.182948:0.452484:0.166450:0.131929:0.166450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f a:@0.177858:0.183064:0.197084:0.183064:0.197084:0.166595:0.177858:0.166595:0.000000:0.000000:0.000000
f b:@0.249948:0.183064:0.269464:0.183064:0.269464:0.166595:0.249948:0.166595:0.000000:0.000000:0.000000
f c:@0.322328:0.183064:0.339763:0.183064:0.339763:0.166595:0.322328:0.166595:0.000000:0.000000:0.000000
f d:@0.392627:0.183064:0.412046:0.183064:0.412046:0.166595:0.392627:0.166595:0.000000:0.000000:0.000000
 :@0.108195:0.200299:0.112337:0.200299:0.112337:0.183801:0.108195:0.183801:0.000000
Se tiene :@0.131929:0.200299:0.192210:0.200299:0.192210:0.183801:0.131929:0.183801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.192307:0.200414:0.226406:0.200414:0.226406:0.183946:0.192307:0.183946:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =   = {1, 2, 3, 4} =   es decir,   es función sobreyec-:@0.216157:0.200299:0.595721:0.200299:0.595721:0.183801:0.216157:0.183801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.251644:0.200414:0.260833:0.200414:0.260833:0.183946:0.251644:0.183946:0.000000
B,:@0.366079:0.200414:0.377985:0.200414:0.377985:0.183946:0.366079:0.183946:0.000000:0.000000
f:@0.442216:0.200414:0.446512:0.200414:0.446512:0.183946:0.442216:0.183946:0.000000
tiva.:@0.131929:0.217649:0.160846:0.217649:0.160846:0.201152:0.131929:0.201152:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.108195:0.235217:0.120466:0.235217:0.120466:0.218503:0.108195:0.218503:0.000000:0.000000
  Consideremos los conjuntos   = {–1, 0, 1, 2},   = {5, 10, 15, 20} :@0.120467:0.235000:0.575970:0.235000:0.575970:0.218503:0.120467:0.218503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.337524:0.235116:0.348794:0.235116:0.348794:0.218647:0.337524:0.218647:0.000000
B:@0.451671:0.235116:0.460860:0.235116:0.460860:0.218647:0.451671:0.218647:0.000000
y   la función de   en   definida como::@0.131929:0.252351:0.409538:0.252351:0.409538:0.235853:0.131929:0.235853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.143893:0.252467:0.151329:0.252467:0.151329:0.235998:0.143893:0.235998:0.000000
A:@0.252393:0.252467:0.263663:0.252467:0.263663:0.235998:0.252393:0.235998:0.000000
B:@0.289498:0.252467:0.298688:0.252467:0.298688:0.235998:0.289498:0.235998:0.000000
 :@0.108195:0.269702:0.112337:0.269702:0.112337:0.253204:0.108195:0.253204:0.000000
g:@0.131929:0.269817:0.139366:0.269817:0.139366:0.253349:0.131929:0.253349:0.000000
(–1) = 20,    (0) = 10,    (1) = 20,    (2) = 10.:@0.139366:0.269702:0.446415:0.269702:0.446415:0.253204:0.139366:0.253204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.221532:0.269817:0.228968:0.269817:0.228968:0.253349:0.221532:0.253349:0.000000
g:@0.300635:0.269817:0.308072:0.269817:0.308072:0.253349:0.300635:0.253349:0.000000
g:@0.379738:0.269817:0.387175:0.269817:0.387175:0.253349:0.379738:0.253349:0.000000
Entonces,:@0.131929:0.287053:0.199934:0.287053:0.199934:0.270555:0.131929:0.270555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec g:@0.204078:0.287168:0.241298:0.287168:0.241298:0.270699:0.204078:0.270699:0.000000:0.000000:0.000000:0.000000:0.000000
( ) = {10, 20} ≠   por lo que   no es sobreyectiva. :@0.227909:0.287053:0.582058:0.287053:0.582058:0.270555:0.227909:0.270555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B,:@0.338029:0.287168:0.349935:0.287168:0.349935:0.270699:0.338029:0.270699:0.000000:0.000000
g:@0.432254:0.287168:0.439690:0.287168:0.439690:0.270699:0.432254:0.270699:0.000000
Función biyectiva:@0.108233:0.323152:0.249293:0.323152:0.249293:0.305469:0.108233:0.305469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.108233:0.340322:0.195100:0.340322:0.195100:0.323376:0.108233:0.323376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean   y   dos conjuntos no vacíos cualesquiera. Una :@0.188319:0.339859:0.599840:0.339859:0.599840:0.323361:0.188319:0.323361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.236964:0.339975:0.248234:0.339975:0.248234:0.323506:0.236964:0.323506:0.000000
B:@0.268462:0.339975:0.277652:0.339975:0.277652:0.323506:0.268462:0.323506:0.000000
función o aplicación   de   en   es biyectiva si y solo si   es inyectiva :@0.108214:0.357210:0.599759:0.357210:0.599759:0.340712:0.108214:0.340712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.258676:0.357326:0.262972:0.357326:0.262972:0.340857:0.258676:0.340857:0.000000
A:@0.290078:0.357326:0.301348:0.357326:0.301348:0.340857:0.290078:0.340857:0.000000
B:@0.328144:0.357326:0.337334:0.357326:0.337334:0.340857:0.328144:0.340857:0.000000
f:@0.504687:0.357326:0.508983:0.357326:0.508983:0.340857:0.504687:0.340857:0.000000
y sobreyectiva. :@0.108214:0.374561:0.216539:0.374561:0.216539:0.358063:0.108214:0.358063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.108214:0.391911:0.116498:0.391911:0.116498:0.375414:0.108214:0.375414:0.000000:0.000000
La negación de la biyectividad de una función se expresa como sigue: :@0.108214:0.409262:0.599875:0.409262:0.599875:0.392764:0.108214:0.392764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una función   de   en   no es biyectiva si y solo si   no es inyectiva o :@0.108214:0.426613:0.599879:0.426613:0.599879:0.410115:0.108214:0.410115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.199127:0.426729:0.203423:0.426729:0.203423:0.410260:0.199127:0.410260:0.000000
A:@0.230258:0.426729:0.241528:0.426729:0.241528:0.410260:0.230258:0.410260:0.000000
B:@0.268056:0.426729:0.277245:0.426729:0.277245:0.410260:0.268056:0.410260:0.000000
f:@0.467353:0.426729:0.471649:0.426729:0.471649:0.410260:0.467353:0.410260:0.000000
f:@0.108214:0.444079:0.112510:0.444079:0.112510:0.427611:0.108214:0.427611:0.000000
 no es sobreyectiva.:@0.112510:0.443964:0.250734:0.443964:0.250734:0.427466:0.112510:0.427466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.108214:0.479041:0.238869:0.479041:0.238869:0.462254:0.108214:0.462254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108214:0.496233:0.120486:0.496233:0.120486:0.479518:0.108214:0.479518:0.000000:0.000000
  Sea   = {–1, 0, 1, 2},   = {5, 10, 15, 20}.:@0.120486:0.496016:0.397271:0.496016:0.397271:0.479518:0.120486:0.479518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.160212:0.496132:0.171482:0.496132:0.171482:0.479663:0.160212:0.479663:0.000000
B:@0.274358:0.496132:0.283548:0.496132:0.283548:0.479663:0.274358:0.479663:0.000000
 :@0.108214:0.513367:0.112356:0.513367:0.112356:0.496869:0.108214:0.496869:0.000000
Se define la función   de   en   como sigue: :@0.131949:0.513367:0.449223:0.513367:0.449223:0.496869:0.131949:0.496869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.276187:0.513482:0.283970:0.513482:0.283970:0.497014:0.276187:0.497014:0.000000
A:@0.310111:0.513482:0.321381:0.513482:0.321381:0.497014:0.310111:0.497014:0.000000
B:@0.347216:0.513482:0.356405:0.513482:0.356405:0.497014:0.347216:0.497014:0.000000
v:@0.196218:0.537961:0.204001:0.537961:0.204001:0.521493:0.196218:0.521493:0.000000
(–1) = 5,     (0) = 10,    (1) = 15,    (2) = 20.:@0.204001:0.537846:0.507738:0.537846:0.507738:0.521348:0.204001:0.521348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.281814:0.537961:0.289597:0.537961:0.289597:0.521493:0.281814:0.521493:0.000000
v:@0.361264:0.537961:0.369047:0.537961:0.369047:0.521493:0.361264:0.521493:0.000000
v:@0.440714:0.537961:0.448497:0.537961:0.448497:0.521493:0.440714:0.521493:0.000000
 :@0.108214:0.567270:0.112356:0.567270:0.112356:0.550772:0.108214:0.550772:0.000000
La función   es inyectiva. Como :@0.131949:0.567270:0.363545:0.567270:0.363545:0.550772:0.131949:0.550772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.212305:0.567385:0.220088:0.567385:0.220088:0.550917:0.212305:0.550917:0.000000
Rec v:@0.363988:0.567385:0.401547:0.567385:0.401547:0.550917:0.363988:0.550917:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =  , la función   es sobre-:@0.387811:0.567270:0.595741:0.567270:0.595741:0.550772:0.387811:0.550772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.427459:0.567385:0.436649:0.567385:0.436649:0.550917:0.427459:0.550917:0.000000
v:@0.519759:0.567385:0.527542:0.567385:0.527542:0.550917:0.519759:0.550917:0.000000
yectiva. Luego,   es una función biyectiva.:@0.131949:0.584620:0.426182:0.584620:0.426182:0.568123:0.131949:0.568123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.239215:0.584736:0.246998:0.584736:0.246998:0.568267:0.239215:0.568267:0.000000
2.:@0.108215:0.602188:0.120487:0.602188:0.120487:0.585474:0.108215:0.585474:0.000000:0.000000
  Se define una función  . Demuestra o refuta que   es biyectiva.:@0.120486:0.601971:0.579647:0.601971:0.579647:0.585474:0.120486:0.585474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.291483:0.602087:0.300692:0.602087:0.300692:0.585618:0.291483:0.585618:0.000000
u:@0.481473:0.602087:0.490682:0.602087:0.490682:0.585618:0.481473:0.585618:0.000000
u:@0.250680:0.631511:0.259889:0.631511:0.259889:0.615043:0.250680:0.615043:0.000000
::@0.259889:0.631396:0.262644:0.631396:0.262644:0.614898:0.259889:0.614898:0.000000
a):@0.108214:0.663075:0.122008:0.663075:0.122008:0.646578:0.108214:0.646578:0.000000:0.000000
 :@0.122009:0.663075:0.126151:0.663075:0.126151:0.646577:0.122009:0.646577:0.000000
Inyectividad:@0.131949:0.663190:0.215368:0.663190:0.215368:0.646722:0.131949:0.646722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108214:0.680426:0.112356:0.680426:0.112356:0.663928:0.108214:0.663928:0.000000
∀:@0.131976:0.688011:0.143549:0.688011:0.143549:0.669012:0.131976:0.669012:0.000000
x x:@0.143557:0.680540:0.170356:0.680540:0.170356:0.664071:0.143557:0.664071:0.000000:0.000000:0.000000
1:@0.151032:0.683701:0.155985:0.683701:0.155985:0.674083:0.151032:0.674083:0.000000
,      ;     ≠      ( ) ≠  ( ).:@0.155984:0.680424:0.377077:0.680424:0.377077:0.663927:0.155984:0.663927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.170356:0.683701:0.175309:0.683701:0.175309:0.674083:0.170356:0.674083:0.000000
:@0.179451:0.679906:0.194103:0.679906:0.194103:0.666532:0.179451:0.666532:0.000000
R:@0.198245:0.679337:0.211550:0.679337:0.211550:0.666475:0.198245:0.666475:0.000000
x:@0.226731:0.680540:0.234206:0.680540:0.234206:0.664071:0.226731:0.664071:0.000000
1:@0.234204:0.683701:0.239158:0.683701:0.239158:0.674083:0.234204:0.674083:0.000000
x:@0.258250:0.680540:0.265725:0.680540:0.265725:0.664071:0.258250:0.664071:0.000000
2:@0.265724:0.683701:0.270677:0.683701:0.270677:0.674083:0.265724:0.674083:0.000000
⇒:@0.274820:0.679918:0.293835:0.679918:0.293835:0.662206:0.274820:0.662206:0.000000
f x:@0.297977:0.680540:0.315701:0.680540:0.315701:0.664071:0.297977:0.664071:0.000000:0.000000:0.000000
1:@0.315696:0.683701:0.320650:0.683701:0.320650:0.674083:0.315696:0.674083:0.000000
f x:@0.345693:0.680540:0.363417:0.680540:0.363417:0.664071:0.345693:0.664071:0.000000:0.000000:0.000000
2:@0.363417:0.683701:0.368370:0.683701:0.368370:0.674083:0.363417:0.674083:0.000000
Supongamos ( ) = f( ), entonces se tiene que::@0.131966:0.697775:0.470448:0.697775:0.470448:0.681277:0.131966:0.681277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.229718:0.697891:0.247442:0.697891:0.247442:0.681422:0.229718:0.681422:0.000000:0.000000:0.000000
1:@0.247450:0.701052:0.252404:0.701052:0.252404:0.691434:0.247450:0.691434:0.000000
x:@0.288141:0.697891:0.295616:0.697891:0.295616:0.681422:0.288141:0.681422:0.000000
2:@0.295614:0.701052:0.300567:0.701052:0.300567:0.691434:0.295614:0.691434:0.000000
–( ) + 1 = –( ) + 1. Por la ley cancelativa:   =  .:@0.131976:0.715126:0.483303:0.715126:0.483303:0.698628:0.131976:0.698628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.148429:0.715241:0.155904:0.715241:0.155904:0.698773:0.148429:0.698773:0.000000
1:@0.155904:0.718402:0.160857:0.718402:0.160857:0.708784:0.155904:0.708784:0.000000
x:@0.229943:0.715241:0.237417:0.715241:0.237417:0.698773:0.229943:0.698773:0.000000
2:@0.237416:0.718402:0.242369:0.718402:0.242369:0.708784:0.237416:0.708784:0.000000
x:@0.436039:0.715241:0.443514:0.715241:0.443514:0.698773:0.436039:0.698773:0.000000
1:@0.443514:0.718402:0.448467:0.718402:0.448467:0.708784:0.443514:0.708784:0.000000
x:@0.467559:0.715241:0.475034:0.715241:0.475034:0.698773:0.467559:0.698773:0.000000
2:@0.475033:0.718402:0.479987:0.718402:0.479987:0.708784:0.475033:0.708784:0.000000
 :@0.108227:0.732477:0.112369:0.732477:0.112369:0.715979:0.108227:0.715979:0.000000
Se comprueba que  ( ) = f( )     =  . Por lo tanto, la función   :@0.131963:0.732477:0.599948:0.732477:0.599948:0.715979:0.131963:0.715979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.269245:0.732592:0.286969:0.732592:0.286969:0.716123:0.269245:0.716123:0.000000:0.000000:0.000000
1:@0.286963:0.735753:0.291916:0.735753:0.291916:0.726135:0.286963:0.726135:0.000000
x:@0.326998:0.732592:0.334473:0.732592:0.334473:0.716123:0.326998:0.716123:0.000000
2:@0.334459:0.735753:0.339412:0.735753:0.339412:0.726135:0.334459:0.726135:0.000000
⇒:@0.349180:0.731970:0.368195:0.731970:0.368195:0.714258:0.349180:0.714258:0.000000
x:@0.371990:0.732592:0.379465:0.732592:0.379465:0.716123:0.371990:0.716123:0.000000
1:@0.379468:0.735753:0.384421:0.735753:0.384421:0.726135:0.379468:0.726135:0.000000
x:@0.402858:0.732592:0.410333:0.732592:0.410333:0.716123:0.402858:0.716123:0.000000
2:@0.410319:0.735753:0.415272:0.735753:0.415272:0.726135:0.410319:0.726135:0.000000
u:@0.586597:0.732592:0.595806:0.732592:0.595806:0.716123:0.586597:0.716123:0.000000
es inyectiva.:@0.131977:0.749827:0.216704:0.749827:0.216704:0.733330:0.131977:0.733330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.108242:0.780755:0.123674:0.780755:0.123674:0.764257:0.108242:0.764257:0.000000:0.000000
 :@0.123674:0.780754:0.127816:0.780754:0.127816:0.764257:0.123674:0.764257:0.000000
Sobreyectiva:@0.131976:0.780870:0.219074:0.780870:0.219074:0.764401:0.131976:0.764401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108242:0.798105:0.112384:0.798105:0.112384:0.781607:0.108242:0.781607:0.000000
Rec u:@0.131976:0.798221:0.170969:0.798221:0.170969:0.781752:0.131976:0.781752:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =  .:@0.155807:0.798105:0.212072:0.798108:0.212072:0.781610:0.155807:0.781607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.196014:0.797021:0.209319:0.797021:0.209319:0.784159:0.196014:0.784159:0.000000
Sean:@0.131968:0.815458:0.165624:0.815458:0.165624:0.798961:0.131968:0.798961:0.000000:0.000000:0.000000:0.000000
z :@0.169766:0.815574:0.180555:0.815574:0.180555:0.799105:0.169766:0.799105:0.000000:0.000000
:@0.180563:0.814940:0.195216:0.814940:0.195216:0.801566:0.180563:0.801566:0.000000
  , entonces :@0.195215:0.815458:0.288411:0.815458:0.288411:0.798961:0.195215:0.798961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.199358:0.814371:0.212662:0.814371:0.212662:0.801509:0.199358:0.801509:0.000000
z  Rec u:@0.288411:0.815574:0.356987:0.815574:0.356987:0.799105:0.288411:0.799105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.299200:0.814940:0.313853:0.814940:0.313853:0.801566:0.299200:0.801566:0.000000
 :@0.313852:0.815458:0.317994:0.815458:0.317994:0.798961:0.313852:0.798961:0.000000
( ), luego   =  ( ), o sea:@0.341825:0.815458:0.510566:0.815458:0.510566:0.798961:0.341825:0.798961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
z u x:@0.413316:0.815574:0.461692:0.815574:0.461692:0.799105:0.413316:0.799105:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108234:0.832809:0.112376:0.832809:0.112376:0.816311:0.108234:0.816311:0.000000
z:@0.131970:0.832925:0.138616:0.832925:0.138616:0.816456:0.131970:0.816456:0.000000
 = –  + 1,    = 1 –  .:@0.138616:0.832809:0.277557:0.832809:0.277557:0.816311:0.138616:0.816311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.168207:0.832925:0.175682:0.832925:0.175682:0.816456:0.168207:0.816456:0.000000
x:@0.214309:0.832925:0.221784:0.832925:0.221784:0.816456:0.214309:0.816456:0.000000
z:@0.268156:0.832925:0.274802:0.832925:0.274802:0.816456:0.268156:0.816456:0.000000
Resulta ( ) =  (1 –  ) + 1 =  ,:@0.131970:0.850160:0.347239:0.850160:0.347239:0.833662:0.131970:0.833662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u x:@0.187608:0.850276:0.210244:0.850276:0.210244:0.833807:0.187608:0.833807:0.000000:0.000000:0.000000
–:@0.235289:0.850276:0.245326:0.850276:0.245326:0.833807:0.235289:0.833807:0.000000
z:@0.278559:0.850276:0.285205:0.850276:0.285205:0.833807:0.278559:0.833807:0.000000
z:@0.337838:0.850276:0.344485:0.850276:0.344485:0.833807:0.337838:0.833807:0.000000
 :@0.108234:0.867511:0.112376:0.867511:0.112376:0.851013:0.108234:0.851013:0.000000
se concluye que   es sobreyectiva.:@0.131970:0.867511:0.373918:0.867511:0.373918:0.851013:0.131970:0.851013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.249832:0.867626:0.259041:0.867626:0.259041:0.851158:0.249832:0.851158:0.000000
 :@0.108234:0.896934:0.112376:0.896934:0.112376:0.880436:0.108234:0.880436:0.000000
Por los literales a y b se :@0.131970:0.896934:0.297531:0.896934:0.297531:0.880436:0.131970:0.880436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ha demostrado que la función  :  :@0.131970:0.914285:0.371221:0.914285:0.371221:0.897787:0.131970:0.897787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.350973:0.914400:0.360182:0.914400:0.360182:0.897932:0.350973:0.897932:0.000000
 :@0.108234:0.943709:0.112376:0.943709:0.112376:0.927211:0.108234:0.927211:0.000000
es inyectiva y sobreyectiva, por lo tanto, es biyectiva.:@0.131970:0.943709:0.503629:0.943709:0.503629:0.927211:0.131970:0.927211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.285277:0.624716:0.298582:0.624716:0.298582:0.611854:0.285277:0.611854:0.000000
    ,:@0.298582:0.625803:0.339067:0.625803:0.339067:0.609306:0.298582:0.609306:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.302724:0.633902:0.318868:0.633902:0.318868:0.614040:0.302724:0.614040:0.000000
R:@0.323007:0.624716:0.336312:0.624716:0.336312:0.611854:0.323007:0.611854:0.000000
x:@0.285278:0.643270:0.292753:0.643270:0.292753:0.626801:0.285278:0.626801:0.000000
    ( ) = –  + 1. :@0.292753:0.643154:0.417322:0.643154:0.417322:0.626656:0.292753:0.626656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.296895:0.651253:0.313039:0.651253:0.313039:0.631390:0.296895:0.631390:0.000000
u x:@0.317182:0.643270:0.339818:0.643270:0.339818:0.626801:0.317182:0.626801:0.000000:0.000000:0.000000
x:@0.375363:0.643270:0.382838:0.643270:0.382838:0.626801:0.375363:0.626801:0.000000
R:@0.385646:0.905858:0.398951:0.905858:0.398951:0.892996:0.385646:0.892996:0.000000
    ,:@0.398951:0.906945:0.439990:0.906945:0.439990:0.890447:0.398951:0.890447:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.403093:0.915044:0.419237:0.915044:0.419237:0.895181:0.403093:0.895181:0.000000
R:@0.423377:0.905858:0.436682:0.905858:0.436682:0.892996:0.423377:0.892996:0.000000
x:@0.385643:0.924411:0.393118:0.924411:0.393118:0.907942:0.385643:0.907942:0.000000
    ( ) = –  + 1:@0.393118:0.924295:0.510790:0.924295:0.510790:0.907798:0.393118:0.907798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.397260:0.932394:0.413404:0.932394:0.413404:0.912532:0.397260:0.912532:0.000000
u x:@0.417546:0.924411:0.440183:0.924411:0.440183:0.907942:0.417546:0.907942:0.000000:0.000000:0.000000
x:@0.475727:0.924411:0.483202:0.924411:0.483202:0.907942:0.475727:0.907942:0.000000
Interdisciplinariedad:@0.684804:0.147175:0.831589:0.147175:0.831589:0.131703:0.684804:0.131703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y Geología:@0.685042:0.176225:0.843739:0.176225:0.843739:0.160753:0.685042:0.160753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En forma general, las funciones :@0.638498:0.191645:0.841556:0.191645:0.841556:0.176582:0.638498:0.176582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(sean estas inyectivas, sobreyec-:@0.638498:0.207487:0.843563:0.207487:0.843563:0.192424:0.638498:0.192424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tivas o biyectivas) son muy uti-:@0.638498:0.223329:0.839725:0.223329:0.839725:0.208266:0.638498:0.208266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lizadas para resolver problemas :@0.638498:0.239171:0.843823:0.239171:0.843823:0.224108:0.638498:0.224108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la vida real. Por ejemplo, en :@0.638498:0.255013:0.837209:0.255013:0.837209:0.239950:0.638498:0.239950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la geología, a fin de determinar :@0.638498:0.270855:0.841783:0.270855:0.841783:0.255792:0.638498:0.255792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la intensidad de un sismo, se :@0.638498:0.286697:0.825848:0.286697:0.825848:0.271634:0.638498:0.271634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
utiliza una función denominada :@0.638498:0.302539:0.849577:0.302539:0.849577:0.287476:0.638498:0.287476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escala de Richter.:@0.638498:0.318381:0.748645:0.318381:0.748645:0.303318:0.638498:0.303318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Investiga escribe:@0.638503:0.460801:0.765605:0.460801:0.765605:0.445329:0.638503:0.445329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.701106:0.460379:0.715811:0.460379:0.715811:0.445316:0.701106:0.445316:0.000000:0.000000:0.000000
 otros ejem-:@0.765609:0.460379:0.843339:0.460379:0.843339:0.445316:0.765609:0.445316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
plos de aplicaciones de estas :@0.638503:0.476221:0.827698:0.476221:0.827698:0.461158:0.638503:0.461158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones.:@0.638503:0.492063:0.704605:0.492063:0.704605:0.477000:0.638503:0.477000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 73497187:@0.871305:0.432284:0.871305:0.367437:0.859836:0.367437:0.859836:0.432284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000