196:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Tipos de funciones: inyectivas, :@0.404235:0.131231:0.784983:0.131231:0.784983:0.086571:0.404235:0.086571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sobreyectivas y biyectivas:@0.404235:0.168950:0.719397:0.168950:0.719397:0.124290:0.404235:0.124290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.23. Reconocer funciones inyectivas, sobreyectivas y biyectivas para calcular la función inversa (de funciones biyectivas) comprobando con la composición de funciones.:@0.143128:0.944754:0.891723:0.944754:0.891723:0.934712:0.143128:0.934712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función inyectiva:@0.404236:0.197121:0.545457:0.197121:0.545457:0.179438:0.404236:0.179438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.404236:0.214291:0.491103:0.214291:0.491103:0.197345:0.404236:0.197345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,   dos conjuntos no vacíos cualesquiera. Se dice :@0.484322:0.213829:0.895943:0.213829:0.895943:0.197331:0.484322:0.197331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.530828:0.213944:0.559167:0.213944:0.559167:0.197475:0.530828:0.197475:0.000000:0.000000:0.000000
que una aplicación   de   en   es inyectiva, o uno a uno, si y solo si se :@0.404236:0.231179:0.895818:0.231179:0.895818:0.214682:0.404236:0.214682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.542116:0.231295:0.546412:0.231295:0.546412:0.214826:0.542116:0.214826:0.000000
A:@0.572168:0.231295:0.583438:0.231295:0.583438:0.214826:0.572168:0.214826:0.000000
B:@0.608887:0.231295:0.618077:0.231295:0.618077:0.214826:0.608887:0.214826:0.000000
verifica la siguiente condición::@0.404236:0.248530:0.616038:0.248530:0.616038:0.232032:0.404236:0.232032:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.526470:0.280595:0.538043:0.280595:0.538043:0.261596:0.526470:0.261596:0.000000
x x:@0.538051:0.273124:0.564850:0.273124:0.564850:0.256655:0.538051:0.256655:0.000000:0.000000:0.000000
1:@0.545526:0.276285:0.550479:0.276285:0.550479:0.266667:0.545526:0.266667:0.000000
,      ,     ≠      ( ) ≠  ( ).:@0.550478:0.273008:0.769537:0.273008:0.769537:0.256511:0.550478:0.256511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.564850:0.276285:0.569803:0.276285:0.569803:0.266667:0.564850:0.266667:0.000000
:@0.573945:0.272490:0.588597:0.272490:0.588597:0.259117:0.573945:0.259117:0.000000
A x:@0.592738:0.273124:0.626664:0.273124:0.626664:0.256655:0.592738:0.256655:0.000000:0.000000:0.000000
1:@0.626664:0.276285:0.631618:0.276285:0.631618:0.266667:0.626664:0.266667:0.000000
x:@0.650708:0.273124:0.658183:0.273124:0.658183:0.256655:0.650708:0.256655:0.000000
2:@0.658184:0.276285:0.663137:0.276285:0.663137:0.266667:0.658184:0.266667:0.000000
⇒:@0.667278:0.272502:0.686293:0.272502:0.686293:0.254790:0.667278:0.254790:0.000000
f x:@0.690435:0.273124:0.708159:0.273124:0.708159:0.256655:0.690435:0.256655:0.000000:0.000000:0.000000
1:@0.708155:0.276285:0.713108:0.276285:0.713108:0.266667:0.708155:0.266667:0.000000
f x:@0.738153:0.273124:0.755877:0.273124:0.755877:0.256655:0.738153:0.256655:0.000000:0.000000:0.000000
2:@0.755876:0.276285:0.760829:0.276285:0.760829:0.266667:0.755876:0.266667:0.000000
En forma equivalente,   es inyectiva si y solo si se verifica: :@0.404229:0.302432:0.806480:0.302432:0.806480:0.285935:0.404229:0.285935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.561991:0.302548:0.566287:0.302548:0.566287:0.286079:0.561991:0.286079:0.000000
∀:@0.526470:0.334494:0.538043:0.334494:0.538043:0.315495:0.526470:0.315495:0.000000
x x:@0.538051:0.327023:0.564850:0.327023:0.564850:0.310555:0.538051:0.310555:0.000000:0.000000:0.000000
1:@0.545526:0.330186:0.550479:0.330186:0.550479:0.320567:0.545526:0.320567:0.000000
,      ,    ( ) =  ( )     =  .:@0.550478:0.326908:0.769536:0.326908:0.769536:0.310410:0.550478:0.310410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.564850:0.330186:0.569803:0.330186:0.569803:0.320567:0.564850:0.320567:0.000000
:@0.573945:0.326389:0.588597:0.326389:0.588597:0.313016:0.573945:0.313016:0.000000
A f x:@0.592738:0.327023:0.636914:0.327023:0.636914:0.310555:0.592738:0.310555:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.636914:0.330186:0.641867:0.330186:0.641867:0.320567:0.636914:0.320567:0.000000
f x:@0.666910:0.327023:0.684634:0.327023:0.684634:0.310555:0.666910:0.310555:0.000000:0.000000:0.000000
2:@0.684634:0.330186:0.689588:0.330186:0.689588:0.320567:0.684634:0.320567:0.000000
⇒:@0.699681:0.326402:0.718696:0.326402:0.718696:0.308689:0.699681:0.308689:0.000000
x:@0.722838:0.327023:0.730313:0.327023:0.730313:0.310555:0.722838:0.310555:0.000000
1:@0.730310:0.330186:0.735263:0.330186:0.735263:0.320567:0.730310:0.320567:0.000000
x:@0.754354:0.327023:0.761829:0.327023:0.761829:0.310555:0.754354:0.310555:0.000000
2:@0.761828:0.330186:0.766781:0.330186:0.766781:0.320567:0.761828:0.320567:0.000000
Esto se lee como: \  es inyectiva si a cada par de elementos distintos :@0.404229:0.356332:0.895816:0.356332:0.895816:0.339834:0.404229:0.339834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.538544:0.356447:0.542840:0.356447:0.542840:0.339979:0.538544:0.339979:0.000000
de   asocia imágenes distintas\. La negación se lee: \la función   no es :@0.404229:0.373682:0.895855:0.373682:0.895855:0.357185:0.404229:0.357185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.426153:0.373798:0.437423:0.373798:0.437423:0.357329:0.426153:0.357329:0.000000
f:@0.845707:0.373798:0.850004:0.373798:0.850004:0.357329:0.845707:0.357329:0.000000
inyectiva si y solo si existen  ,       tal que   ≠  , pero  ( ) =  ( )\. :@0.404229:0.391033:0.895912:0.391030:0.895912:0.374532:0.404229:0.374536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.596993:0.391149:0.623497:0.391146:0.623497:0.374677:0.596993:0.374680:0.000000:0.000000:0.000000
1:@0.604481:0.394308:0.609434:0.394308:0.609434:0.384690:0.604481:0.384690:0.000000
2:@0.623497:0.394308:0.628450:0.394308:0.628450:0.384690:0.623497:0.384690:0.000000
:@0.632285:0.390511:0.646937:0.390511:0.646937:0.377138:0.632285:0.377138:0.000000
A,:@0.650770:0.391146:0.665277:0.391146:0.665277:0.374677:0.650770:0.374677:0.000000:0.000000
x:@0.721782:0.391146:0.729257:0.391146:0.729257:0.374677:0.721782:0.374677:0.000000
1:@0.729259:0.394308:0.734213:0.394308:0.734213:0.384690:0.729259:0.384690:0.000000
x:@0.752687:0.391146:0.760162:0.391146:0.760162:0.374677:0.752687:0.374677:0.000000
2:@0.760164:0.394308:0.765117:0.394308:0.765117:0.384690:0.760164:0.384690:0.000000
f x:@0.808367:0.391146:0.826091:0.391146:0.826091:0.374677:0.808367:0.374677:0.000000:0.000000:0.000000
1:@0.826092:0.394308:0.831045:0.394308:0.831045:0.384690:0.826092:0.384690:0.000000
f x:@0.855472:0.391146:0.873196:0.391146:0.873196:0.374677:0.855472:0.374677:0.000000:0.000000:0.000000
2:@0.873198:0.394308:0.878151:0.394308:0.878151:0.384690:0.873198:0.384690:0.000000
Ejercicios resueltos:@0.404244:0.426107:0.534899:0.426107:0.534899:0.409321:0.404244:0.409321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404244:0.443299:0.416516:0.443299:0.416516:0.426585:0.404244:0.426585:0.000000:0.000000
  Sean   = { ,  ,  ,  },   = {1, 2, 3, 4} y   la función de   en   definida :@0.416516:0.443082:0.895814:0.443082:0.895814:0.426585:0.416516:0.426585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.465392:0.443198:0.476662:0.443198:0.476662:0.426729:0.465392:0.426729:0.000000
a b c d B:@0.500840:0.443198:0.576552:0.443198:0.576552:0.426729:0.500840:0.426729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.675441:0.443198:0.684842:0.443198:0.684842:0.426729:0.675441:0.426729:0.000000
A:@0.784364:0.443198:0.795635:0.443198:0.795635:0.426729:0.784364:0.426729:0.000000
B:@0.820699:0.443198:0.829888:0.443198:0.829888:0.426729:0.820699:0.426729:0.000000
como sigue: :@0.427959:0.460433:0.516637:0.460433:0.516637:0.443935:0.427959:0.443935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h a:@0.506677:0.485028:0.531009:0.485028:0.531009:0.468559:0.506677:0.468559:0.000000:0.000000:0.000000
( ) = 3,     ( ) = 1,    ( ) = 4,    ( ) = 2.:@0.516079:0.484912:0.789298:0.484912:0.789298:0.468414:0.516079:0.468414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h b:@0.583873:0.485028:0.608494:0.485028:0.608494:0.468559:0.583873:0.468559:0.000000:0.000000:0.000000
h c:@0.657216:0.485028:0.679756:0.485028:0.679756:0.468559:0.657216:0.468559:0.000000:0.000000:0.000000
h d:@0.728478:0.485028:0.753003:0.485028:0.753003:0.468559:0.728478:0.468559:0.000000:0.000000:0.000000
   Primeramente, observamos que   define una función de   en  . :@0.404224:0.514336:0.895912:0.514336:0.895912:0.497838:0.404224:0.497838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.663205:0.514452:0.672607:0.514452:0.672607:0.497983:0.663205:0.497983:0.000000
A:@0.841758:0.514452:0.853028:0.514452:0.853028:0.497983:0.841758:0.497983:0.000000
B:@0.879633:0.514452:0.888823:0.514452:0.888823:0.497983:0.879633:0.497983:0.000000
Esta función es inyectiva, pues a cada par de elementos distintos :@0.427979:0.531687:0.895966:0.531687:0.895966:0.515189:0.427979:0.515189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del conjunto  , asocia imágenes distintas. Por ejemplo,   ≠   y :@0.427979:0.549038:0.895912:0.549038:0.895912:0.532540:0.427979:0.532540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.527734:0.549153:0.539004:0.549153:0.539004:0.532684:0.527734:0.532684:0.000000
a:@0.838194:0.549153:0.847171:0.549153:0.847171:0.532684:0.838194:0.532684:0.000000
b:@0.869114:0.549153:0.878381:0.549153:0.878381:0.532684:0.869114:0.532684:0.000000
h a:@0.427979:0.566504:0.452696:0.566504:0.452696:0.550035:0.427979:0.550035:0.000000:0.000000:0.000000
( ) = 3 ≠  ( ) = 1.:@0.437573:0.566388:0.569520:0.566388:0.569520:0.549891:0.437573:0.549891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h b:@0.507062:0.566504:0.532069:0.566504:0.532069:0.550035:0.507062:0.550035:0.000000:0.000000:0.000000
2.:@0.404244:0.583956:0.416516:0.583956:0.416516:0.567241:0.404244:0.567241:0.000000:0.000000
  Nuevamente, consideremos los conjuntos   = { ,  ,  ,  },:@0.416516:0.583739:0.830156:0.583739:0.830156:0.567241:0.416516:0.567241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.730035:0.583855:0.741305:0.583855:0.741305:0.567386:0.730035:0.567386:0.000000
a b c d:@0.766253:0.583855:0.821545:0.583855:0.821545:0.567386:0.766253:0.567386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404244:0.601090:0.408386:0.601090:0.408386:0.584592:0.404244:0.584592:0.000000
B:@0.427979:0.601206:0.437168:0.601206:0.437168:0.584737:0.427979:0.584737:0.000000
 = {1, 2, 3, 4} y   la función de   en   definida como se indica: :@0.437168:0.601090:0.876312:0.601090:0.876312:0.584592:0.437168:0.584592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.538754:0.601206:0.547963:0.601206:0.547963:0.584737:0.538754:0.584737:0.000000
A:@0.649026:0.601206:0.660296:0.601206:0.660296:0.584737:0.649026:0.584737:0.000000
B:@0.686129:0.601206:0.695319:0.601206:0.695319:0.584737:0.686129:0.584737:0.000000
u a:@0.507082:0.625685:0.531221:0.625685:0.531221:0.609216:0.507082:0.609216:0.000000:0.000000:0.000000
( ) = 2,     ( ) = 3,    ( ) = 2,    ( ) = 4.:@0.516290:0.625569:0.788932:0.625569:0.788932:0.609071:0.516290:0.609071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u b:@0.584085:0.625685:0.608513:0.625685:0.608513:0.609216:0.584085:0.609216:0.000000:0.000000:0.000000
u c:@0.657235:0.625685:0.679583:0.625685:0.679583:0.609216:0.657235:0.609216:0.000000:0.000000:0.000000
u d:@0.728305:0.625685:0.752637:0.625685:0.752637:0.609216:0.728305:0.609216:0.000000:0.000000:0.000000
 :@0.404244:0.654993:0.408386:0.654993:0.408386:0.638495:0.404244:0.638495:0.000000
Esta función no es inyectiva ya que   ≠  , pero  ( ) =  ( ) = 2.:@0.427979:0.654993:0.868190:0.654993:0.868190:0.638495:0.427979:0.638495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.680272:0.655109:0.689250:0.655109:0.689250:0.638640:0.680272:0.638640:0.000000
c:@0.709116:0.655109:0.716302:0.655109:0.716302:0.638640:0.709116:0.638640:0.000000
u a:@0.760362:0.655109:0.784501:0.655109:0.784501:0.638640:0.760362:0.638640:0.000000:0.000000:0.000000
u c:@0.809546:0.655109:0.831894:0.655109:0.831894:0.638640:0.809546:0.638640:0.000000:0.000000:0.000000
Función sobreyectiva:@0.404236:0.691086:0.574144:0.691086:0.574144:0.673403:0.404236:0.673403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.404236:0.708256:0.491103:0.708256:0.491103:0.691310:0.404236:0.691310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,   dos conjuntos no vacíos cualesquiera. Una fun-:@0.484322:0.707793:0.891817:0.707793:0.891817:0.691296:0.484322:0.691296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.528131:0.707909:0.555102:0.707909:0.555102:0.691440:0.528131:0.691440:0.000000:0.000000:0.000000
ción   de   en   es sobreyectiva si y solo si :@0.404236:0.725144:0.705909:0.725144:0.705909:0.708646:0.404236:0.708646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.439280:0.725260:0.443576:0.725260:0.443576:0.708791:0.439280:0.708791:0.000000
A:@0.469719:0.725260:0.480989:0.725260:0.480989:0.708791:0.469719:0.708791:0.000000
B:@0.506824:0.725260:0.516013:0.725260:0.516013:0.708791:0.506824:0.708791:0.000000
Rec f:@0.705909:0.725260:0.739991:0.725260:0.739991:0.708791:0.705909:0.708791:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =  .:@0.729742:0.725144:0.776980:0.725144:0.776980:0.708646:0.729742:0.708646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.765036:0.725260:0.774225:0.725260:0.774225:0.708791:0.765036:0.708791:0.000000
La igualdad de los conjuntos :@0.404236:0.754568:0.617192:0.754568:0.617192:0.738070:0.404236:0.738070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.618772:0.754684:0.652816:0.754684:0.652816:0.738215:0.618772:0.738215:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =   significa las dos inclusiones :@0.642567:0.754568:0.895963:0.754568:0.895963:0.738070:0.642567:0.738070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.681020:0.754684:0.690210:0.754684:0.690210:0.738215:0.681020:0.738215:0.000000
siguientes: :@0.404236:0.771919:0.480739:0.771919:0.480739:0.755421:0.404236:0.755421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.480218:0.772034:0.514299:0.772034:0.514299:0.755566:0.480218:0.755566:0.000000:0.000000:0.000000:0.000000:0.000000
( )     y     :@0.504049:0.771919:0.600819:0.771919:0.600819:0.755421:0.504049:0.755421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.523873:0.771702:0.539921:0.771702:0.539921:0.757055:0.523873:0.757055:0.000000
B B:@0.543543:0.772034:0.576988:0.772034:0.576988:0.755566:0.543543:0.755566:0.000000:0.000000:0.000000
:@0.580629:0.771702:0.596677:0.771702:0.596677:0.757055:0.580629:0.757055:0.000000
Rec f:@0.600299:0.772034:0.634379:0.772034:0.634379:0.755566:0.600299:0.755566:0.000000:0.000000:0.000000:0.000000:0.000000
( ). De la definición del conjunto reco-:@0.624130:0.771919:0.891684:0.771919:0.891684:0.755421:0.624130:0.755421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rrido de  , se tiene :@0.404198:0.789269:0.534951:0.789269:0.534951:0.772772:0.404198:0.772772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.465114:0.789385:0.469411:0.789385:0.469411:0.772916:0.465114:0.772916:0.000000
Rec f:@0.535067:0.789385:0.569185:0.789385:0.569185:0.772916:0.535067:0.772916:0.000000:0.000000:0.000000:0.000000:0.000000
( )    . De la inclusión     :@0.558936:0.789269:0.758582:0.789269:0.758582:0.772772:0.558936:0.772772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.579396:0.789053:0.595444:0.789053:0.595444:0.774406:0.579396:0.774406:0.000000
B:@0.599701:0.789385:0.608891:0.789385:0.608891:0.772916:0.599701:0.772916:0.000000
B:@0.724906:0.789385:0.734096:0.789385:0.734096:0.772916:0.724906:0.772916:0.000000
:@0.738392:0.789053:0.754440:0.789053:0.754440:0.774406:0.738392:0.774406:0.000000
Rec f:@0.758698:0.789385:0.792778:0.789385:0.792778:0.772916:0.758698:0.772916:0.000000:0.000000:0.000000:0.000000:0.000000
( ), se sigue que :@0.782529:0.789269:0.895828:0.789269:0.895828:0.772772:0.782529:0.772772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.404178:0.806736:0.411865:0.806736:0.411865:0.790267:0.404178:0.790267:0.000000
           :@0.411865:0.806620:0.501364:0.806617:0.501364:0.790119:0.411865:0.790123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.415944:0.806098:0.430597:0.806098:0.430597:0.792725:0.415944:0.792725:0.000000
B:@0.434623:0.806733:0.443812:0.806733:0.443812:0.790264:0.434623:0.790264:0.000000
⇒:@0.447838:0.806111:0.466853:0.806111:0.466853:0.788399:0.447838:0.788399:0.000000
y:@0.470880:0.806733:0.478567:0.806733:0.478567:0.790264:0.470880:0.790264:0.000000
:@0.482570:0.806098:0.497223:0.806098:0.497223:0.792725:0.482570:0.792725:0.000000
Rec f:@0.501248:0.806733:0.535329:0.806733:0.535329:0.790264:0.501248:0.790264:0.000000:0.000000:0.000000:0.000000:0.000000
( ), y por la definición del conjunto :@0.525080:0.806617:0.775293:0.806617:0.775293:0.790119:0.525080:0.790119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.775177:0.806733:0.809223:0.806733:0.809223:0.790264:0.775177:0.790264:0.000000:0.000000:0.000000:0.000000:0.000000
( ), se tiene la :@0.798974:0.806617:0.895936:0.806617:0.895936:0.790119:0.798974:0.790119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
equivalencia siguiente::@0.404248:0.823968:0.561840:0.823968:0.561840:0.807470:0.404248:0.807470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.517181:0.848562:0.524868:0.848562:0.524868:0.832094:0.517181:0.832094:0.000000
   :@0.524868:0.848447:0.547798:0.848446:0.547798:0.831949:0.524868:0.831949:0.000000:0.000000:0.000000
:@0.529005:0.847928:0.543657:0.847928:0.543657:0.834554:0.529005:0.834554:0.000000
Rec f:@0.547798:0.848562:0.581879:0.848562:0.581879:0.832093:0.547798:0.832093:0.000000:0.000000:0.000000:0.000000:0.000000
( ) :@0.571629:0.848446:0.591974:0.848446:0.591974:0.831949:0.571629:0.831949:0.000000:0.000000:0.000000:0.000000
⇔:@0.591974:0.847940:0.612048:0.847940:0.612048:0.830228:0.591974:0.830228:0.000000
 :@0.612048:0.848446:0.616190:0.848446:0.616190:0.831949:0.612048:0.831949:0.000000
∃:@0.616189:0.855520:0.626515:0.855520:0.626515:0.837385:0.616189:0.837385:0.000000
x  A:@0.626512:0.848562:0.668194:0.848562:0.668194:0.832093:0.626512:0.832093:0.000000:0.000000:0.000000:0.000000
:@0.638130:0.847928:0.652782:0.847928:0.652782:0.834554:0.638130:0.834554:0.000000
   tal que   =  ( ).:@0.652781:0.848446:0.778832:0.848446:0.778832:0.831949:0.652781:0.831949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y f x:@0.725622:0.848562:0.770124:0.848562:0.770124:0.832093:0.725622:0.832093:0.000000:0.000000:0.000000:0.000000:0.000000
Por lo tanto, la sobreyectividad de la función   puede ser expresada :@0.404240:0.877870:0.895924:0.877870:0.895924:0.861373:0.404240:0.861373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.734520:0.877986:0.738816:0.877986:0.738816:0.861517:0.734520:0.861517:0.000000
con la siguiente equivalencia: :@0.404240:0.895221:0.613055:0.895221:0.613055:0.878723:0.404240:0.878723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.489219:0.919816:0.523300:0.919816:0.523300:0.903347:0.489219:0.903347:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =   :@0.513051:0.919700:0.561676:0.919700:0.561676:0.903202:0.513051:0.903202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.548344:0.919816:0.557534:0.919816:0.557534:0.903347:0.548344:0.903347:0.000000
⇔:@0.561676:0.919194:0.581750:0.919194:0.581750:0.901482:0.561676:0.901482:0.000000
 :@0.581750:0.919700:0.585892:0.919700:0.585892:0.903202:0.581750:0.903202:0.000000
∀:@0.585892:0.927283:0.597465:0.927283:0.597465:0.908284:0.585892:0.908284:0.000000
y  B,  x  A:@0.597472:0.919812:0.696148:0.919812:0.696148:0.903344:0.597472:0.903344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.609301:0.919178:0.623953:0.919178:0.623953:0.905805:0.609301:0.905805:0.000000
 :@0.623954:0.919697:0.628096:0.919697:0.628096:0.903199:0.623954:0.903199:0.000000
∃:@0.644144:0.926771:0.654469:0.926771:0.654469:0.908635:0.644144:0.908635:0.000000
:@0.666083:0.919178:0.680735:0.919178:0.680735:0.905805:0.666083:0.905805:0.000000
   tal que   =  ( ).:@0.680736:0.919697:0.806789:0.919697:0.806789:0.903199:0.680736:0.903199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y f x:@0.753578:0.919812:0.798081:0.919812:0.798081:0.903344:0.753578:0.903344:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.112146:0.307805:0.112146:0.307805:0.096673:0.199646:0.096673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es una función?:@0.199884:0.140773:0.338335:0.140773:0.338335:0.125710:0.199884:0.125710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.191963:0.363493:0.191963:0.363493:0.176490:0.199646:0.176490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es la diferencia:@0.199884:0.220590:0.331862:0.220590:0.331862:0.205527:0.199884:0.205527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre función inyectiva y:@0.153341:0.236432:0.313197:0.236432:0.313197:0.221369:0.153341:0.221369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sobreyectiva?:@0.153341:0.252274:0.239829:0.252274:0.239829:0.237211:0.153341:0.237211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.486657:0.297267:0.486657:0.297267:0.471184:0.199644:0.471184:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.499225:0.283707:0.499225:0.283707:0.483752:0.199644:0.483752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una de las primeras ta-:@0.199880:0.523699:0.348973:0.523699:0.348973:0.508636:0.199880:0.508636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reas en el estudio de funciones :@0.153337:0.539541:0.354687:0.539541:0.354687:0.524478:0.153337:0.524478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es el reconocimiento del tipo :@0.153337:0.555383:0.345313:0.555383:0.345313:0.540320:0.153337:0.540320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de función que corresponde; :@0.153337:0.571225:0.343200:0.571225:0.343200:0.556162:0.153337:0.556162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es decir, distinguir si la función :@0.153337:0.587067:0.352314:0.587067:0.352314:0.572004:0.153337:0.572004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es inyectiva, sobreyectiva o :@0.153337:0.602909:0.331081:0.602909:0.331081:0.587846:0.153337:0.587846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
biyectiva. En este último caso, :@0.153337:0.618751:0.348954:0.618751:0.348954:0.603688:0.153337:0.603688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es posible determinar o definir :@0.153337:0.634593:0.353948:0.634593:0.353948:0.619530:0.153337:0.619530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función inversa.:@0.153337:0.650435:0.269007:0.650435:0.269007:0.635372:0.153337:0.635372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000