32:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Números reales y funciones:@0.073089:0.043661:0.318030:0.043661:0.318030:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.1 Función inyectiva:@0.293660:0.231541:0.459278:0.231541:0.459278:0.214594:0.293660:0.214594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.293660:0.259971:0.371734:0.259971:0.371734:0.243301:0.293660:0.243301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.371652:0.259971:0.379751:0.259971:0.379751:0.243024:0.371652:0.243024:0.000000:0.000000
Sean  ,   dos conjuntos no vacíos cualesquiera. Se dice que una aplicación :@0.380064:0.259971:0.930511:0.259971:0.930511:0.244258:0.380064:0.244258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.419952:0.259971:0.446127:0.259971:0.446127:0.244535:0.419952:0.244535:0.000000:0.000000:0.000000
o función   de   en   es inyectiva, o uno a uno, si y solo si se verifica la siguiente condición::@0.293660:0.276612:0.927013:0.276612:0.927013:0.260900:0.293660:0.260900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.365025:0.276612:0.369719:0.276612:0.369719:0.261177:0.365025:0.261177:0.000000
A:@0.394937:0.276612:0.404822:0.276612:0.404822:0.261177:0.394937:0.261177:0.000000
B:@0.429911:0.276612:0.438746:0.276612:0.438746:0.261177:0.429911:0.261177:0.000000
;:@0.487360:0.304488:0.499637:0.304488:0.499637:0.290772:0.487360:0.290772:0.000000
x x:@0.499545:0.305042:0.526634:0.305054:0.526634:0.289618:0.499545:0.289607:0.000000:0.000000:0.000000
1:@0.506922:0.308226:0.512158:0.308226:0.512158:0.299065:0.506922:0.299065:0.000000
,      ,            ( )    ( ).:@0.512111:0.305054:0.733232:0.305054:0.733232:0.289341:0.512111:0.289341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.526572:0.308226:0.531809:0.308226:0.531809:0.299065:0.526572:0.299065:0.000000
[:@0.535712:0.304764:0.550348:0.304764:0.550348:0.291354:0.535712:0.291354:0.000000
A x:@0.554218:0.305054:0.586449:0.305054:0.586449:0.289618:0.554218:0.289618:0.000000:0.000000:0.000000
1:@0.586392:0.308226:0.591629:0.308226:0.591629:0.299065:0.586392:0.299065:0.000000
±:@0.595541:0.305595:0.610874:0.305595:0.610874:0.290423:0.595541:0.290423:0.000000
x:@0.614740:0.305054:0.622194:0.305054:0.622194:0.289618:0.614740:0.289618:0.000000
2:@0.622114:0.308226:0.627351:0.308226:0.627351:0.299065:0.622114:0.299065:0.000000
⇒:@0.631261:0.304638:0.649429:0.304638:0.649429:0.287649:0.631261:0.287649:0.000000
f x:@0.653294:0.305054:0.670174:0.305054:0.670174:0.289618:0.653294:0.289618:0.000000:0.000000:0.000000
1:@0.670092:0.308226:0.675329:0.308226:0.675329:0.299065:0.670092:0.299065:0.000000
±:@0.684024:0.305595:0.699358:0.305595:0.699358:0.290423:0.684024:0.290423:0.000000
f x:@0.703223:0.305054:0.720103:0.305054:0.720103:0.289618:0.703223:0.289618:0.000000:0.000000:0.000000
2:@0.720034:0.308226:0.725271:0.308226:0.725271:0.299065:0.720034:0.299065:0.000000
En forma equivalente,   es inyectiva si y solo si se verifica: :@0.293667:0.333483:0.704719:0.333483:0.704719:0.317771:0.293667:0.317771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.455172:0.333483:0.459866:0.333483:0.459866:0.318048:0.455172:0.318048:0.000000
;:@0.487330:0.361359:0.499607:0.361359:0.499607:0.347643:0.487330:0.347643:0.000000
x x:@0.499515:0.361913:0.526634:0.361923:0.526634:0.346488:0.499515:0.346478:0.000000:0.000000:0.000000
1:@0.506922:0.365096:0.512158:0.365096:0.512158:0.355935:0.506922:0.355935:0.000000
,      ,    ( )    ( )        .:@0.512111:0.361923:0.733224:0.361923:0.733224:0.346211:0.512111:0.346211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.526572:0.365096:0.531809:0.365096:0.531809:0.355935:0.526572:0.355935:0.000000
[:@0.535712:0.361633:0.550348:0.361633:0.550348:0.348223:0.535712:0.348223:0.000000
A f x:@0.554218:0.361923:0.595874:0.361923:0.595874:0.346488:0.554218:0.346488:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.595819:0.365096:0.601055:0.365096:0.601055:0.355935:0.595819:0.355935:0.000000
5:@0.609751:0.361369:0.625084:0.361369:0.625084:0.347653:0.609751:0.347653:0.000000
f x:@0.628950:0.361923:0.645829:0.361923:0.645829:0.346488:0.628950:0.346488:0.000000:0.000000:0.000000
2:@0.645761:0.365096:0.650998:0.365096:0.650998:0.355935:0.645761:0.355935:0.000000
⇒:@0.659695:0.361507:0.677863:0.361507:0.677863:0.344519:0.659695:0.344519:0.000000
x:@0.681729:0.361923:0.689183:0.361923:0.689183:0.346488:0.681729:0.346488:0.000000
1:@0.689110:0.365096:0.694347:0.365096:0.694347:0.355935:0.689110:0.355935:0.000000
5:@0.698258:0.361369:0.713591:0.361369:0.713591:0.347653:0.698258:0.347653:0.000000
x:@0.717457:0.361923:0.724912:0.361923:0.724912:0.346488:0.717457:0.346488:0.000000
2:@0.724832:0.365096:0.730069:0.365096:0.730069:0.355935:0.724832:0.355935:0.000000
Esto se lee como \  es inyectiva si a cada par de elementos distintos de   asocia imágenes :@0.293658:0.390353:0.930844:0.390353:0.930844:0.374640:0.293658:0.374640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.422104:0.390353:0.426798:0.390353:0.426798:0.374918:0.422104:0.374918:0.000000
A:@0.794962:0.390353:0.804846:0.390353:0.804846:0.374918:0.794962:0.374918:0.000000
distintas\. La negación se lee: \la función   no es inyectiva si y solo si existen  ,       tal :@0.293658:0.406995:0.930958:0.407001:0.930958:0.391289:0.293658:0.391282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.586702:0.406995:0.591396:0.406995:0.591396:0.391560:0.586702:0.391560:0.000000
x x:@0.837225:0.406995:0.864392:0.407001:0.864392:0.391566:0.837225:0.391560:0.000000:0.000000:0.000000
1:@0.844623:0.410174:0.849860:0.410174:0.849860:0.401013:0.844623:0.401013:0.000000
2:@0.864318:0.410174:0.869555:0.410174:0.869555:0.401013:0.864318:0.401013:0.000000
[:@0.873504:0.406711:0.888140:0.406711:0.888140:0.393301:0.873504:0.393301:0.000000
A,:@0.892046:0.407001:0.905189:0.407001:0.905189:0.391566:0.892046:0.391566:0.000000:0.000000
que      , pero  ( )    ( )\. :@0.293663:0.423643:0.506665:0.423643:0.506665:0.407930:0.293663:0.407930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.326042:0.423643:0.333497:0.423643:0.333497:0.408208:0.326042:0.408208:0.000000
1:@0.333435:0.426816:0.338672:0.426816:0.338672:0.417655:0.333435:0.417655:0.000000
±:@0.342582:0.424184:0.357915:0.424184:0.357915:0.409012:0.342582:0.409012:0.000000
x:@0.361780:0.423643:0.369235:0.423643:0.369235:0.408208:0.361780:0.408208:0.000000
2:@0.369155:0.426816:0.374392:0.426816:0.374392:0.417655:0.369155:0.417655:0.000000
f x:@0.419149:0.423643:0.436029:0.423643:0.436029:0.408208:0.419149:0.408208:0.000000:0.000000:0.000000
1:@0.435967:0.426816:0.441203:0.426816:0.441203:0.417655:0.435967:0.417655:0.000000
5:@0.449901:0.423088:0.465234:0.423088:0.465234:0.409373:0.449901:0.409373:0.000000
f x:@0.469100:0.423643:0.485979:0.423643:0.485979:0.408208:0.469100:0.408208:0.000000:0.000000:0.000000
2:@0.485911:0.426816:0.491147:0.426816:0.491147:0.417655:0.485911:0.417655:0.000000
Ejercicios resueltos:@0.293663:0.452073:0.436673:0.452073:0.436673:0.435403:0.293663:0.435403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.  Sean     { ,  ,  ,  },     {1, 2, 3, 4} y   la función de   en   definida como sigue: :@0.293660:0.480513:0.900075:0.480513:0.900075:0.464800:0.293660:0.464800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.363191:0.480513:0.373076:0.480513:0.373076:0.465077:0.363191:0.465077:0.000000
5:@0.376960:0.479958:0.392293:0.479958:0.392293:0.466242:0.376960:0.466242:0.000000
a b c d B:@0.400944:0.480513:0.477997:0.480513:0.477997:0.465077:0.400944:0.465077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.481881:0.479958:0.497214:0.479958:0.497214:0.466242:0.481881:0.466242:0.000000
h:@0.583415:0.480513:0.592914:0.480513:0.592914:0.465077:0.583415:0.465077:0.000000
A:@0.695129:0.480513:0.705014:0.480513:0.705014:0.465077:0.695129:0.465077:0.000000
B:@0.731465:0.480513:0.740300:0.480513:0.740300:0.465077:0.731465:0.465077:0.000000
h a:@0.479506:0.508943:0.502994:0.508943:0.502994:0.493507:0.479506:0.493507:0.000000:0.000000:0.000000
( )   3,     ( )   1,    ( )   4,    ( )   2.:@0.488931:0.508943:0.771004:0.508943:0.771004:0.493230:0.488931:0.493230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.511664:0.508388:0.526997:0.508388:0.526997:0.494672:0.511664:0.494672:0.000000
h b:@0.558676:0.508943:0.582164:0.508943:0.582164:0.493507:0.558676:0.493507:0.000000:0.000000:0.000000
5:@0.590834:0.508388:0.606167:0.508388:0.606167:0.494672:0.590834:0.494672:0.000000
h c:@0.633906:0.508943:0.655793:0.508943:0.655793:0.493507:0.633906:0.493507:0.000000:0.000000:0.000000
5:@0.664463:0.508388:0.679796:0.508388:0.679796:0.494672:0.664463:0.494672:0.000000
h d:@0.707536:0.508943:0.731023:0.508943:0.731023:0.493507:0.707536:0.493507:0.000000:0.000000:0.000000
5:@0.739693:0.508388:0.755026:0.508388:0.755026:0.494672:0.739693:0.494672:0.000000
Primeramente, observamos que   define una función de   en  . Esta función es :@0.323671:0.537372:0.930908:0.537372:0.930908:0.521660:0.323671:0.521660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.569904:0.537372:0.579403:0.537372:0.579403:0.521937:0.569904:0.521937:0.000000
A:@0.756977:0.537372:0.766862:0.537372:0.766862:0.521937:0.756977:0.521937:0.000000
B:@0.795890:0.537372:0.804726:0.537372:0.804726:0.521937:0.795890:0.521937:0.000000
inyectiva, pues a cada par de elementos distintos del conjunto   asocia imágenes :@0.323652:0.554014:0.930908:0.554014:0.930908:0.538302:0.323652:0.538302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.789963:0.554014:0.799848:0.554014:0.799848:0.538579:0.789963:0.538579:0.000000
distintas. Por ejemplo,       y  ( )   3    ( )   1.:@0.323634:0.570656:0.699123:0.570656:0.699123:0.554943:0.323634:0.554943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.489833:0.570656:0.499092:0.570656:0.499092:0.555221:0.489833:0.555221:0.000000
±:@0.503344:0.571197:0.518677:0.571197:0.518677:0.556025:0.503344:0.556025:0.000000
b h a:@0.522911:0.570656:0.572610:0.570656:0.572610:0.555221:0.522911:0.555221:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.581832:0.570101:0.597166:0.570101:0.597166:0.556386:0.581832:0.556386:0.000000
±:@0.614616:0.571197:0.629949:0.571197:0.629949:0.556025:0.614616:0.556025:0.000000
h b:@0.634183:0.570656:0.658038:0.570656:0.658038:0.555221:0.634183:0.555221:0.000000:0.000000:0.000000
5:@0.667260:0.570101:0.682594:0.570101:0.682594:0.556386:0.667260:0.556386:0.000000
2.  Nuevamente, consideremos los conjuntos:@0.293660:0.599102:0.629344:0.599102:0.629344:0.583390:0.293660:0.583390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     { ,  ,  ,  },:@0.629052:0.599102:0.737489:0.599102:0.737489:0.582433:0.629052:0.582433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.632881:0.599102:0.642765:0.599102:0.642765:0.583667:0.632881:0.583667:0.000000
5:@0.646520:0.598548:0.661854:0.598548:0.661854:0.584832:0.646520:0.584832:0.000000
a b c d:@0.670744:0.599102:0.728598:0.599102:0.728598:0.583667:0.670744:0.583667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.293660:0.627538:0.297691:0.627538:0.297691:0.611826:0.293660:0.611826:0.000000
B:@0.323781:0.627538:0.332617:0.627538:0.332617:0.612103:0.323781:0.612103:0.000000
   {1, 2, 3, 4} y   la función de   en   definida como se indica: :@0.332543:0.627538:0.778753:0.627538:0.778753:0.611826:0.332543:0.611826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.336500:0.626984:0.351834:0.626984:0.351834:0.613268:0.336500:0.613268:0.000000
u:@0.438035:0.627538:0.447349:0.627538:0.447349:0.612103:0.438035:0.612103:0.000000
A:@0.549564:0.627538:0.559449:0.627538:0.559449:0.612103:0.549564:0.612103:0.000000
B:@0.585900:0.627538:0.594736:0.627538:0.594736:0.612103:0.585900:0.612103:0.000000
u a:@0.479930:0.655968:0.503233:0.655968:0.503233:0.640533:0.479930:0.640533:0.000000:0.000000:0.000000
( )   2,     ( )   3,    ( )   2,    ( )   4.:@0.489170:0.655968:0.770691:0.655968:0.770691:0.640255:0.489170:0.640255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.511903:0.655413:0.527236:0.655413:0.527236:0.641698:0.511903:0.641698:0.000000
u b:@0.558915:0.655968:0.582219:0.655968:0.582219:0.640533:0.558915:0.640533:0.000000:0.000000:0.000000
5:@0.590889:0.655413:0.606222:0.655413:0.606222:0.641698:0.590889:0.641698:0.000000
u c:@0.633962:0.655968:0.655664:0.655968:0.655664:0.640533:0.633962:0.640533:0.000000:0.000000:0.000000
5:@0.664334:0.655413:0.679667:0.655413:0.679667:0.641698:0.664334:0.641698:0.000000
u d:@0.707407:0.655968:0.730710:0.655968:0.730710:0.640533:0.707407:0.640533:0.000000:0.000000:0.000000
5:@0.739380:0.655413:0.754713:0.655413:0.754713:0.641698:0.739380:0.641698:0.000000
Esta función no es inyectiva, ya que      , pero  ( )    ( )   2.:@0.323726:0.684398:0.781974:0.684398:0.781974:0.668685:0.323726:0.668685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.583471:0.684398:0.592729:0.684398:0.592729:0.668963:0.583471:0.668963:0.000000
±:@0.596982:0.684939:0.612315:0.684939:0.612315:0.669767:0.596982:0.669767:0.000000
c:@0.616548:0.684398:0.624206:0.684398:0.624206:0.668963:0.616548:0.668963:0.000000
u a:@0.669120:0.684398:0.692423:0.684398:0.692423:0.668963:0.669120:0.668963:0.000000:0.000000:0.000000
5:@0.701093:0.683843:0.716426:0.683843:0.716426:0.670128:0.701093:0.670128:0.000000
u c:@0.720292:0.684398:0.741994:0.684398:0.741994:0.668963:0.720292:0.668963:0.000000:0.000000:0.000000
5:@0.750664:0.683843:0.765997:0.683843:0.765997:0.670128:0.750664:0.670128:0.000000
3.2 Función sobreyectiva:@0.293593:0.712828:0.488692:0.712828:0.488692:0.695881:0.293593:0.695881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.293593:0.741258:0.372060:0.741258:0.372060:0.724588:0.293593:0.724588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.372008:0.741258:0.380144:0.741258:0.380144:0.724311:0.372008:0.724311:0.000000:0.000000
Sean  ,   dos conjuntos no vacíos cualesquiera. Una función   de   en   es :@0.380494:0.741258:0.930887:0.741258:0.930887:0.725545:0.380494:0.725545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.420585:0.741258:0.446870:0.741258:0.446870:0.725822:0.420585:0.725822:0.000000:0.000000:0.000000
f:@0.828011:0.741258:0.832705:0.741258:0.832705:0.725822:0.828011:0.725822:0.000000
A:@0.860408:0.741258:0.870292:0.741258:0.870292:0.725822:0.860408:0.725822:0.000000
B:@0.897848:0.741258:0.906684:0.741258:0.906684:0.725822:0.897848:0.725822:0.000000
sobreyectiva si y solo si :@0.293593:0.757899:0.464330:0.757899:0.464330:0.742187:0.293593:0.742187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.464100:0.757899:0.497785:0.757899:0.497785:0.742464:0.464100:0.742464:0.000000:0.000000:0.000000:0.000000:0.000000
( )    .:@0.488287:0.757899:0.537618:0.757899:0.537618:0.742187:0.488287:0.742187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.506455:0.757345:0.521788:0.757345:0.521788:0.743629:0.506455:0.743629:0.000000
B:@0.525653:0.757899:0.534489:0.757899:0.534489:0.742464:0.525653:0.742464:0.000000
La igualdad de los conjuntos :@0.293593:0.786329:0.504413:0.786329:0.504413:0.770617:0.293593:0.770617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.503859:0.786329:0.537545:0.786329:0.537545:0.770894:0.503859:0.770894:0.000000:0.000000:0.000000:0.000000:0.000000
( )     significa las dos inclusiones siguientes: :@0.528046:0.786329:0.857761:0.786329:0.857761:0.770617:0.528046:0.770617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.545901:0.785774:0.561235:0.785774:0.561235:0.772059:0.545901:0.772059:0.000000
B:@0.564769:0.786329:0.573604:0.786329:0.573604:0.770894:0.564769:0.770894:0.000000
Rec f:@0.857113:0.786329:0.890798:0.786329:0.890798:0.770894:0.857113:0.770894:0.000000:0.000000:0.000000:0.000000:0.000000
( )     :@0.881300:0.786329:0.930889:0.786329:0.930889:0.770617:0.881300:0.770617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.899155:0.786191:0.914488:0.786191:0.914488:0.772142:0.899155:0.772142:0.000000
B:@0.918022:0.786329:0.926858:0.786329:0.926858:0.770894:0.918022:0.770894:0.000000
y     :@0.293612:0.802971:0.336114:0.802971:0.336114:0.787258:0.293612:0.787258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.304895:0.802971:0.313731:0.802971:0.313731:0.787536:0.304895:0.787536:0.000000
,:@0.316952:0.802832:0.332285:0.802832:0.332285:0.788784:0.316952:0.788784:0.000000
Rec f:@0.335451:0.802971:0.368805:0.802971:0.368805:0.787536:0.335451:0.787536:0.000000:0.000000:0.000000:0.000000:0.000000
( ). De la definición del conjunto recorrido de  , se tiene :@0.359399:0.802971:0.748823:0.802971:0.748823:0.787258:0.359399:0.787258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.678728:0.802971:0.683422:0.802971:0.683422:0.787536:0.678728:0.787536:0.000000
Rec f:@0.748216:0.802971:0.781569:0.802971:0.781569:0.787536:0.748216:0.787536:0.000000:0.000000:0.000000:0.000000:0.000000
( )    . De la inclusión :@0.772163:0.802971:0.930804:0.802971:0.930804:0.787258:0.772163:0.787258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.789485:0.802832:0.804818:0.802832:0.804818:0.788784:0.789485:0.788784:0.000000
B:@0.807984:0.802971:0.816819:0.802971:0.816819:0.787536:0.807984:0.787536:0.000000
B:@0.293612:0.819613:0.302447:0.819613:0.302447:0.804178:0.293612:0.804178:0.000000
   :@0.302355:0.819613:0.325106:0.819613:0.325106:0.803900:0.302355:0.803900:0.000000:0.000000:0.000000
,:@0.305871:0.819474:0.321204:0.819474:0.321204:0.805426:0.305871:0.805426:0.000000
Rec f:@0.324591:0.819613:0.358184:0.819613:0.358184:0.804178:0.324591:0.804178:0.000000:0.000000:0.000000:0.000000:0.000000
( ), se sigue que             :@0.348705:0.819613:0.555123:0.819639:0.555123:0.803927:0.348705:0.803900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.462848:0.819613:0.470321:0.819613:0.470321:0.804178:0.462848:0.804178:0.000000
[:@0.473807:0.819349:0.488443:0.819349:0.488443:0.805939:0.473807:0.805939:0.000000
B:@0.491841:0.819639:0.500676:0.819639:0.500676:0.804204:0.491841:0.804204:0.000000
⇒:@0.504100:0.819223:0.522268:0.819223:0.522268:0.802235:0.504100:0.802235:0.000000
y:@0.525655:0.819639:0.533128:0.819639:0.533128:0.804204:0.525655:0.804204:0.000000
[:@0.536574:0.819349:0.551210:0.819349:0.551210:0.805939:0.536574:0.805939:0.000000
Rec f:@0.554608:0.819639:0.588196:0.819639:0.588196:0.804204:0.554608:0.804204:0.000000:0.000000:0.000000:0.000000:0.000000
( ), y por la definición del conjunto :@0.578722:0.819639:0.826554:0.819639:0.826554:0.803927:0.578722:0.803927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.826110:0.819639:0.859703:0.819639:0.859703:0.804204:0.826110:0.804204:0.000000:0.000000:0.000000:0.000000:0.000000
( ), se tiene :@0.850224:0.819639:0.930921:0.819639:0.930921:0.803927:0.850224:0.803927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la equivalencia siguiente::@0.293662:0.836281:0.475297:0.836281:0.475297:0.820569:0.293662:0.820569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.480679:0.864711:0.488153:0.864711:0.488153:0.849276:0.480679:0.849276:0.000000
   :@0.488079:0.864711:0.510623:0.864717:0.510623:0.849005:0.488079:0.848998:0.000000:0.000000:0.000000
[:@0.492043:0.864427:0.506680:0.864427:0.506680:0.851017:0.492043:0.851017:0.000000
Rec f:@0.510549:0.864717:0.544235:0.864717:0.544235:0.849282:0.510549:0.849282:0.000000:0.000000:0.000000:0.000000:0.000000
( ) :@0.534737:0.864717:0.552997:0.864717:0.552997:0.849005:0.534737:0.849005:0.000000:0.000000:0.000000:0.000000
⇔:@0.552905:0.864301:0.572085:0.864301:0.572085:0.847313:0.552905:0.847313:0.000000
 :@0.571993:0.864717:0.576024:0.864717:0.576024:0.849005:0.571993:0.849005:0.000000
':@0.575944:0.864030:0.587663:0.864030:0.587663:0.850938:0.575944:0.850938:0.000000
x :@0.587575:0.864717:0.598270:0.864717:0.598270:0.849282:0.587575:0.849282:0.000000:0.000000
[:@0.598211:0.864427:0.612848:0.864427:0.612848:0.851017:0.598211:0.851017:0.000000
   tal que      ( ).:@0.612760:0.864717:0.739899:0.864717:0.739899:0.849005:0.612760:0.849005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.616717:0.864717:0.626602:0.864717:0.626602:0.849282:0.616717:0.849282:0.000000
y:@0.684530:0.864717:0.692003:0.864717:0.692003:0.849282:0.684530:0.849282:0.000000
5:@0.695887:0.864163:0.711220:0.864163:0.711220:0.850447:0.695887:0.850447:0.000000
f x:@0.715086:0.864717:0.731965:0.864717:0.731965:0.849282:0.715086:0.849282:0.000000:0.000000:0.000000
Por lo tanto, la sobreyectividad de la función   puede ser expresada con la siguiente :@0.293670:0.893147:0.931086:0.893147:0.931086:0.877434:0.293670:0.877434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.635824:0.893147:0.640518:0.893147:0.640518:0.877712:0.635824:0.877712:0.000000
equivalencia: :@0.293689:0.909789:0.392351:0.909789:0.392351:0.894076:0.293689:0.894076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec f:@0.451512:0.938219:0.485198:0.938219:0.485198:0.922783:0.451512:0.922783:0.000000:0.000000:0.000000:0.000000:0.000000
( )     :@0.475699:0.938219:0.525859:0.938219:0.525859:0.922506:0.475699:0.922506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.493867:0.937664:0.509201:0.937664:0.509201:0.923948:0.493867:0.923948:0.000000
B:@0.513066:0.938219:0.521902:0.938219:0.521902:0.922783:0.513066:0.922783:0.000000
⇔:@0.525786:0.937803:0.544966:0.937803:0.544966:0.920814:0.525786:0.920814:0.000000
 :@0.544874:0.938219:0.548905:0.938219:0.548905:0.922506:0.544874:0.922506:0.000000
;:@0.548832:0.937664:0.561109:0.937664:0.561109:0.923948:0.548832:0.923948:0.000000
y :@0.561017:0.938219:0.571730:0.938219:0.571730:0.922783:0.561017:0.922783:0.000000:0.000000
[:@0.571640:0.937939:0.586276:0.937939:0.586276:0.924530:0.571640:0.924530:0.000000
 :@0.586188:0.938229:0.590219:0.938229:0.590219:0.922517:0.586188:0.922517:0.000000
B,  x :@0.590146:0.938229:0.627471:0.938229:0.627471:0.922794:0.590146:0.922794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
':@0.605144:0.937542:0.616864:0.937542:0.616864:0.924450:0.605144:0.924450:0.000000
[:@0.627412:0.937939:0.642048:0.937939:0.642048:0.924530:0.627412:0.924530:0.000000
   tal que      ( ).:@0.641961:0.938229:0.769099:0.938229:0.769099:0.922517:0.641961:0.922517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.645918:0.938229:0.655803:0.938229:0.655803:0.922794:0.645918:0.922794:0.000000
y:@0.713730:0.938229:0.721204:0.938229:0.721204:0.922794:0.713730:0.922794:0.000000
5:@0.725088:0.937675:0.740421:0.937675:0.740421:0.923959:0.725088:0.923959:0.000000
f x:@0.744286:0.938229:0.761166:0.938229:0.761166:0.922794:0.744286:0.922794:0.000000:0.000000:0.000000
Tema 3. Tipos de funciones :@0.073089:0.098522:0.476840:0.098522:0.476840:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es una función?:@0.293660:0.167374:0.449404:0.167374:0.449404:0.151661:0.293660:0.151661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función:@0.107782:0.183924:0.136449:0.183924:0.136449:0.176160:0.107782:0.176160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
No es una función:@0.188280:0.183924:0.252678:0.183924:0.252678:0.176160:0.188280:0.176160:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
No es una función:@0.188280:0.271182:0.252678:0.271182:0.252678:0.263418:0.188280:0.263418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función:@0.107130:0.271182:0.135798:0.271182:0.135798:0.263418:0.107130:0.263418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una de las primeras tareas :@0.082576:0.347977:0.257883:0.347977:0.257883:0.333693:0.082576:0.333693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el estudio de funciones :@0.082576:0.363106:0.259503:0.363106:0.259503:0.348822:0.082576:0.348822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es el reconocimiento :@0.082576:0.378235:0.223999:0.378235:0.223999:0.363951:0.082576:0.363951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del tipo de función que :@0.082576:0.393364:0.240627:0.393364:0.240627:0.379080:0.082576:0.379080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
corresponde; es decir, :@0.082576:0.408493:0.228845:0.408493:0.228845:0.394208:0.082576:0.394208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distinguir si la función es :@0.082576:0.423622:0.247496:0.423622:0.247496:0.409337:0.082576:0.409337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inyectiva, sobreyectiva :@0.082576:0.438751:0.233855:0.438751:0.233855:0.424466:0.082576:0.424466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o biyectiva. En este :@0.082576:0.453880:0.211007:0.453880:0.211007:0.439595:0.082576:0.439595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
último caso, es posible :@0.082576:0.469008:0.234680:0.469008:0.234680:0.454724:0.082576:0.454724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinar o definir la :@0.082576:0.484137:0.231728:0.484137:0.231728:0.469853:0.082576:0.469853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función inversa.:@0.082576:0.499266:0.185343:0.499266:0.185343:0.484982:0.082576:0.484982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.304693:0.187141:0.304693:0.187141:0.287746:0.078581:0.287746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.321335:0.176057:0.321335:0.176057:0.304388:0.078581:0.304388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t.ly/abrqG:@0.104396:0.932345:0.176287:0.932345:0.176287:0.916633:0.104396:0.916633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Funciones :@0.080269:0.800890:0.164352:0.800890:0.164352:0.783943:0.080269:0.783943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inyectivas:@0.080269:0.817531:0.158988:0.817531:0.158988:0.800584:0.080269:0.800584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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