43:@0.921538:0.966074:0.940353:0.966074:0.940353:0.949450:0.921538:0.949450:0.000000:0.000000
2.:@0.108233:0.098372:0.120505:0.098372:0.120505:0.081658:0.108233:0.081658:0.000000:0.000000
  Consideremos :@0.120506:0.098156:0.237944:0.098156:0.237944:0.081658:0.120506:0.081658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A = :@0.237946:0.098271:0.268385:0.098271:0.268385:0.081803:0.237946:0.081803:0.000000:0.000000:0.000000:0.000000
R:@0.268393:0.097069:0.281697:0.097069:0.281697:0.084206:0.268393:0.084206:0.000000
,:@0.281696:0.100190:0.285043:0.100190:0.285043:0.080857:0.281696:0.080857:0.000000
 :@0.285043:0.098156:0.289185:0.098156:0.289185:0.081658:0.285043:0.081658:0.000000
 f, g:@0.289185:0.098271:0.312053:0.098271:0.312053:0.081803:0.289185:0.081803:0.000000:0.000000:0.000000:0.000000:0.000000
 las funciones reales definidas como:@0.312053:0.098156:0.565907:0.098156:0.565907:0.081658:0.312053:0.081658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108227:0.119743:0.112369:0.119743:0.112369:0.103246:0.108227:0.103246:0.000000
f(x) :@0.131961:0.119859:0.158740:0.119859:0.158740:0.103390:0.131961:0.103390:0.000000:0.000000:0.000000:0.000000:0.000000
= :@0.158740:0.119743:0.173690:0.119743:0.173690:0.103246:0.158740:0.103246:0.000000:0.000000
1:@0.176984:0.112326:0.185480:0.112326:0.185480:0.095828:0.176984:0.095828:0.000000
4:@0.176984:0.128665:0.185480:0.128665:0.185480:0.112167:0.176984:0.112167:0.000000
x  , g(x) = x :@0.191717:0.119860:0.271596:0.119860:0.271596:0.103392:0.191717:0.103392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.199192:0.113460:0.203898:0.113460:0.203898:0.103859:0.199192:0.103859:0.000000
– 2,:@0.271596:0.119745:0.297488:0.119745:0.297488:0.103247:0.271596:0.103247:0.000000:0.000000:0.000000:0.000000
    x :@0.297488:0.119860:0.325673:0.119860:0.325673:0.103392:0.297488:0.103392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.325671:0.119226:0.344721:0.119226:0.344721:0.105853:0.325671:0.105853:0.000000:0.000000
R:@0.344720:0.118658:0.358025:0.118658:0.358025:0.105796:0.344720:0.105796:0.000000
. :@0.358025:0.119860:0.365018:0.119860:0.365018:0.103392:0.358025:0.103392:0.000000:0.000000
La función:@0.365018:0.119745:0.440363:0.119745:0.440363:0.103247:0.365018:0.103247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.440363:0.119424:0.444145:0.119424:0.444145:0.104361:0.440363:0.104361:0.000000
f + g:@0.444144:0.119860:0.475045:0.119860:0.475045:0.103392:0.444144:0.103392:0.000000:0.000000:0.000000:0.000000:0.000000
 se define como:@0.475045:0.119745:0.588518:0.119745:0.588518:0.103247:0.475045:0.103247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108235:0.149632:0.112377:0.149632:0.112377:0.133134:0.108235:0.133134:0.000000
(f + g)(x) = f(x) + g (x) =  x  + x – 2,   x :@0.131970:0.149748:0.414682:0.149748:0.414682:0.133279:0.131970:0.133279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.305434:0.142330:0.313506:0.142330:0.313506:0.125861:0.305434:0.125861:0.000000
4:@0.305434:0.158669:0.313506:0.158669:0.313506:0.142200:0.305434:0.142200:0.000000
2 :@0.327629:0.143348:0.334750:0.143348:0.334750:0.133747:0.327629:0.133747:0.000000:0.000000
 :@0.414680:0.149113:0.433730:0.149113:0.433730:0.135740:0.414680:0.135740:0.000000:0.000000
R:@0.433730:0.148545:0.447035:0.148545:0.447035:0.135683:0.433730:0.135683:0.000000
.:@0.447035:0.149748:0.449886:0.149748:0.449886:0.133279:0.447035:0.133279:0.000000
 :@0.108236:0.187356:0.112378:0.187356:0.112378:0.170858:0.108236:0.170858:0.000000
Calculemos algunos valores de:@0.131971:0.187356:0.349106:0.187356:0.349106:0.170858:0.131971:0.170858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f(x), g(x)     (f + g) (x), x:@0.349106:0.187472:0.511766:0.187472:0.511766:0.171003:0.349106:0.171003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.416943:0.187356:0.424765:0.187356:0.424765:0.170858:0.416943:0.170858:0.000000
 :@0.511765:0.188128:0.516627:0.188128:0.516627:0.168795:0.511765:0.168795:0.000000
 :@0.516626:0.186832:0.535676:0.186832:0.535676:0.173459:0.516626:0.173459:0.000000:0.000000
R:@0.535677:0.186264:0.548982:0.186264:0.548982:0.173402:0.535677:0.173402:0.000000
.:@0.548980:0.187467:0.551831:0.187467:0.551831:0.170998:0.548980:0.170998:0.000000
En la Figura 2.2. se muestran las gráficas de las funciones :@0.108230:0.378209:0.507997:0.378209:0.507997:0.361712:0.108230:0.361712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f, g   f + g. :@0.507997:0.378325:0.580845:0.378325:0.580845:0.361856:0.507997:0.361856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.530871:0.378209:0.538693:0.378209:0.538693:0.361712:0.530871:0.361712:0.000000
Demostración propiedades de la adición de funciones:@0.108233:0.414308:0.537982:0.414308:0.537982:0.396626:0.108233:0.396626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.537982:0.413665:0.542124:0.413665:0.542124:0.397168:0.537982:0.397168:0.000000
Se demuestra la propiedad conmutativa de la adición de funciones :@0.108232:0.431016:0.599953:0.431016:0.599953:0.414518:0.108232:0.414518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.595759:0.431016:0.599901:0.431016:0.599901:0.414518:0.595759:0.414518:0.000000
y el resto de propiedades se deja como tarea para el estudiante.:@0.108232:0.448367:0.555853:0.448367:0.555853:0.431869:0.108232:0.431869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i.:@0.108232:0.483285:0.115842:0.483285:0.115842:0.466571:0.108232:0.466571:0.000000:0.000000
  Sean:@0.115842:0.483068:0.165624:0.483068:0.165624:0.466571:0.115842:0.466571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f, g   F(A). :@0.165624:0.483184:0.248118:0.483184:0.248118:0.466715:0.165624:0.466715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.192642:0.482550:0.207294:0.482550:0.207294:0.469176:0.192642:0.469176:0.000000
Entonces, de la definición de :@0.248118:0.483068:0.455543:0.483068:0.455543:0.466571:0.248118:0.466571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f + g,:@0.455543:0.483184:0.489415:0.483184:0.489415:0.466715:0.455543:0.466715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 se tiene: :@0.489415:0.483068:0.554723:0.483068:0.554723:0.466571:0.489415:0.466571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(f + g) (x) = f (x) + g (x) = g (x) + f (x) = (g + f) (x)     x   A,:@0.146301:0.507663:0.557708:0.507664:0.557708:0.491195:0.146301:0.491194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.524408:0.507029:0.539060:0.507029:0.539060:0.493656:0.524408:0.493656:0.000000
 :@0.108230:0.532026:0.112372:0.532026:0.112372:0.515529:0.108230:0.515529:0.000000
y por la definición de igualdad de funciones se concluye que:  :@0.131964:0.532026:0.571590:0.532026:0.571590:0.515529:0.131964:0.515529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108230:0.549377:0.112372:0.549377:0.112372:0.532879:0.108230:0.532879:0.000000
f + g  =  g + f.:@0.131964:0.549493:0.223494:0.549493:0.223494:0.533024:0.131964:0.533024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resta:@0.108233:0.585476:0.151716:0.585476:0.151716:0.567793:0.108233:0.567793:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.602646:0.188317:0.602646:0.188317:0.585700:0.108233:0.585700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  :@0.188319:0.602184:0.237829:0.602184:0.237829:0.585686:0.188319:0.585686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f, g   F(A).:@0.238158:0.602299:0.312797:0.602299:0.312797:0.585831:0.238158:0.585831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.261127:0.601665:0.275780:0.601665:0.275780:0.588292:0.261127:0.588292:0.000000
 Como  :@0.312797:0.602184:0.370901:0.602184:0.370901:0.585686:0.312797:0.585686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–g   F(A) y  f   F(A),:@0.371238:0.602299:0.523574:0.602299:0.523574:0.585831:0.371238:0.585831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.393188:0.601665:0.407840:0.601665:0.407840:0.588292:0.393188:0.588292:0.000000
:@0.471902:0.601665:0.486555:0.601665:0.486555:0.588292:0.471902:0.588292:0.000000
 entonces, :@0.523574:0.602184:0.599913:0.602184:0.599913:0.585686:0.523574:0.585686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
        :@0.108244:0.622556:0.141380:0.622556:0.141380:0.606059:0.108244:0.606059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  + (–g)   F A:@0.141380:0.622672:0.243215:0.622668:0.243215:0.606199:0.141380:0.606203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.201455:0.622033:0.216108:0.622033:0.216108:0.608660:0.201455:0.608660:0.000000
  :@0.243214:0.623193:0.252939:0.623193:0.252939:0.603826:0.243214:0.603826:0.000000:0.000000
que se define como::@0.252939:0.622552:0.396174:0.622552:0.396174:0.606054:0.252939:0.606054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(f + (–g) (x) = f (x) + (–g) (x) = f (x) – g (x),    x   A,:@0.171736:0.647147:0.532260:0.647146:0.532260:0.630677:0.171736:0.630678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.498959:0.646512:0.513612:0.646512:0.513612:0.633138:0.498959:0.633138:0.000000
y que se notará como :@0.108231:0.674531:0.273834:0.674531:0.273834:0.658034:0.108231:0.658034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 f – g.:@0.275529:0.674647:0.317776:0.674647:0.317776:0.658178:0.275529:0.658178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.317811:0.675303:0.322673:0.675303:0.322673:0.655970:0.317811:0.655970:0.000000
La resta de funciones reales se define :@0.324667:0.674526:0.599887:0.674526:0.599887:0.658029:0.324667:0.658029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como:  :@0.108241:0.691877:0.161067:0.691877:0.161067:0.675379:0.108241:0.675379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f – g = f + (–g).:@0.300066:0.712365:0.403944:0.712365:0.403944:0.695897:0.300066:0.695897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Producto de funciones:@0.108233:0.748344:0.289700:0.748344:0.289700:0.730662:0.108233:0.730662:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.108233:0.765515:0.188317:0.765515:0.188317:0.748569:0.108233:0.748569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean :@0.188319:0.765052:0.234680:0.765052:0.234680:0.748554:0.188319:0.748554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f, g   F(A). :@0.236347:0.765168:0.319111:0.765168:0.319111:0.748699:0.236347:0.748699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.261968:0.764533:0.276621:0.764533:0.276621:0.751160:0.261968:0.751160:0.000000
El producto de   por   se nota :@0.320777:0.765052:0.548252:0.765052:0.548252:0.748554:0.320777:0.748554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.435907:0.765168:0.440203:0.765168:0.440203:0.748699:0.435907:0.748699:0.000000
g:@0.477115:0.765168:0.484551:0.765168:0.484551:0.748699:0.477115:0.748699:0.000000
fg :@0.549899:0.765168:0.565889:0.765168:0.565889:0.748699:0.549899:0.748699:0.000000:0.000000:0.000000
y se :@0.567546:0.765052:0.599883:0.765052:0.599883:0.748554:0.567546:0.748554:0.000000:0.000000:0.000000:0.000000:0.000000
define como::@0.108205:0.782403:0.201581:0.782403:0.201581:0.765905:0.108205:0.765905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fg x:@0.263575:0.800013:0.297175:0.800013:0.297175:0.783967:0.263575:0.783967:0.000000:0.000000:0.000000:0.000000
( )( ):@0.252811:0.801276:0.305258:0.801276:0.305258:0.781109:0.252811:0.781109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.306826:0.799900:0.317356:0.799900:0.317356:0.783827:0.306826:0.783827:0.000000
f x g x:@0.323099:0.800013:0.378588:0.800013:0.378588:0.783967:0.323099:0.783967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.329830:0.801276:0.386663:0.801276:0.386663:0.781109:0.329830:0.781109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.386663:0.801309:0.389347:0.801309:0.389347:0.782182:0.386663:0.782182:0.000000
x:@0.407451:0.800013:0.414734:0.800013:0.414734:0.783967:0.407451:0.783967:0.000000
.:@0.445127:0.800595:0.447811:0.800595:0.447811:0.784522:0.445127:0.784522:0.000000
A:@0.405816:0.783993:0.394929:0.783993:0.394929:0.797314:0.405816:0.797314:0.000000
A:@0.430884:0.800619:0.442949:0.800619:0.442949:0.783847:0.430884:0.783847:0.000000
Los :@0.108233:0.825277:0.136110:0.825277:0.136110:0.808779:0.108233:0.808779:0.000000:0.000000:0.000000:0.000000
argumentos:@0.139250:0.825494:0.227733:0.825494:0.227733:0.808779:0.139250:0.808779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  que  intervienen  en el  producto  de  las  funciones:@0.227735:0.825277:0.595767:0.825277:0.595767:0.808779:0.227735:0.808779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  g:@0.108233:0.843365:0.131833:0.843365:0.131833:0.826896:0.108233:0.826896:0.000000:0.000000:0.000000:0.000000
y   son:  :@0.114552:0.843249:0.168493:0.843249:0.168493:0.826751:0.114552:0.826751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom(f) = Dom(g) = A, :@0.166375:0.843365:0.320532:0.843365:0.320532:0.826896:0.166375:0.826896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para cada:@0.318417:0.843249:0.385238:0.843249:0.385238:0.826751:0.318417:0.826751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x A f x g x:@0.388988:0.843372:0.503374:0.843372:0.503374:0.826903:0.388988:0.826903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.427474:0.843256:0.430229:0.843256:0.430229:0.826758:0.427474:0.826758:0.000000
( ) ( ):@0.446678:0.844669:0.511660:0.844669:0.511660:0.823970:0.446678:0.823970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.472068:0.843256:0.474823:0.843256:0.474823:0.826758:0.472068:0.826758:0.000000
. Luego, :@0.542376:0.843256:0.599909:0.843256:0.599909:0.826758:0.542376:0.826758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.595759:0.843256:0.599901:0.843256:0.599901:0.826758:0.595759:0.826758:0.000000
f x g x:@0.114641:0.862223:0.174223:0.862223:0.174223:0.844994:0.114641:0.844994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) ( ):@0.121870:0.863580:0.182895:0.863580:0.182895:0.841926:0.121870:0.841926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.213773:0.860149:0.218380:0.860149:0.218380:0.847286:0.213773:0.847286:0.000000
es la imagen de la función   en :@0.219518:0.861235:0.446886:0.861235:0.446886:0.844738:0.219518:0.844738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fg:@0.409011:0.861351:0.420666:0.861351:0.420666:0.844882:0.409011:0.844882:0.000000:0.000000
x   A:@0.447888:0.861351:0.491184:0.861351:0.491184:0.844882:0.447888:0.844882:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.460295:0.860717:0.474947:0.860717:0.474947:0.847344:0.460295:0.847344:0.000000
 que se escribe  :@0.490992:0.861235:0.599998:0.861235:0.599998:0.844738:0.490992:0.844738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.595791:0.861235:0.599933:0.861235:0.599933:0.844738:0.595791:0.844738:0.000000
(fg) (x).:@0.108230:0.878702:0.154736:0.878702:0.154736:0.862233:0.108230:0.862233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Resulta  :@0.154543:0.878586:0.218273:0.878586:0.218273:0.862089:0.154543:0.862089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fg   F(A). :@0.218273:0.878702:0.289739:0.878702:0.289739:0.862233:0.218273:0.862233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.234265:0.878068:0.248917:0.878068:0.248917:0.864694:0.234265:0.864694:0.000000
Se tiene la implicación:  :@0.108241:0.913288:0.282455:0.913288:0.282455:0.896790:0.108241:0.896790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f, g   F(A)     fg   F(A),:@0.283495:0.913403:0.465634:0.913403:0.465634:0.896935:0.283495:0.896935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.307823:0.912769:0.322475:0.912769:0.322475:0.899396:0.307823:0.899396:0.000000
⇒:@0.367694:0.912643:0.385882:0.912643:0.385882:0.895701:0.367694:0.895701:0.000000
:@0.413259:0.912769:0.427912:0.912769:0.427912:0.899396:0.413259:0.899396:0.000000
 que se denomina :@0.465634:0.913288:0.599932:0.913288:0.599932:0.896790:0.465634:0.896790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedad clausurativa.:@0.108225:0.930638:0.273230:0.930638:0.273230:0.914141:0.108225:0.914141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.158338:0.226761:0.166815:0.226761:0.166815:0.209815:0.158338:0.209815:0.000000
f(x) =   x:@0.207541:0.226761:0.276010:0.226761:0.276010:0.209815:0.207541:0.209815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.254125:0.221729:0.263507:0.221729:0.263507:0.204784:0.254125:0.204784:0.000000
2:@0.276018:0.220215:0.281488:0.220215:0.281488:0.210336:0.276018:0.210336:0.000000
       4:@0.225736:0.234053:0.263303:0.234053:0.263303:0.217108:0.225736:0.217108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g(x)= x – 2:@0.306920:0.226766:0.389163:0.226766:0.389163:0.209820:0.306920:0.209820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.389163:0.226361:0.393710:0.226361:0.393710:0.209806:0.389163:0.209806:0.000000
(f + g)(x) =    x  + x –2:@0.410875:0.226766:0.581896:0.226761:0.581896:0.209815:0.410875:0.209820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.502790:0.221734:0.512172:0.221734:0.512172:0.204789:0.502790:0.204789:0.000000
2:@0.524661:0.220215:0.530131:0.220215:0.530131:0.210336:0.524661:0.210336:0.000000
     :@0.481621:0.239080:0.501753:0.239080:0.501753:0.222134:0.481621:0.222134:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.501753:0.234048:0.511135:0.234048:0.511135:0.217103:0.501753:0.217103:0.000000
–2:@0.154570:0.257402:0.170580:0.257402:0.170580:0.243725:0.154570:0.243725:0.000000:0.000000
1:@0.240185:0.260014:0.248854:0.260014:0.248854:0.243459:0.240185:0.243459:0.000000
–:@0.339274:0.259363:0.348122:0.259363:0.348122:0.245687:0.339274:0.245687:0.000000
4:@0.348122:0.260014:0.356792:0.260014:0.356792:0.243459:0.348122:0.243459:0.000000
–:@0.487621:0.259363:0.496470:0.259363:0.496470:0.245687:0.487621:0.245687:0.000000
3:@0.496470:0.260014:0.505139:0.260014:0.505139:0.243459:0.496470:0.243459:0.000000
–1:@0.152893:0.281356:0.172274:0.281356:0.172274:0.264800:0.152893:0.264800:0.000000:0.000000
1/4:@0.232632:0.281356:0.256425:0.281356:0.256425:0.264800:0.232632:0.264800:0.000000:0.000000:0.000000
–:@0.339274:0.280699:0.348122:0.280699:0.348122:0.267023:0.339274:0.267023:0.000000
3:@0.348122:0.281351:0.356792:0.281351:0.356792:0.264795:0.348122:0.264795:0.000000
–:@0.475724:0.280699:0.484572:0.280699:0.484572:0.267023:0.475724:0.267023:0.000000
11/4:@0.484572:0.281351:0.517034:0.281351:0.517034:0.264795:0.484572:0.264795:0.000000:0.000000:0.000000:0.000000
0:@0.158238:0.302692:0.166907:0.302692:0.166907:0.286137:0.158238:0.286137:0.000000
0:@0.240173:0.302692:0.248843:0.302692:0.248843:0.286137:0.240173:0.286137:0.000000
–:@0.339274:0.302036:0.348122:0.302036:0.348122:0.288359:0.339274:0.288359:0.000000
2:@0.348122:0.302687:0.356792:0.302687:0.356792:0.286132:0.348122:0.286132:0.000000
–:@0.480059:0.302036:0.488908:0.302036:0.488908:0.288359:0.480059:0.288359:0.000000
2/3:@0.488908:0.302687:0.512700:0.302687:0.512700:0.286132:0.488908:0.286132:0.000000:0.000000:0.000000
1:@0.158239:0.324028:0.166908:0.324028:0.166908:0.307473:0.158239:0.307473:0.000000
1/4:@0.232622:0.324028:0.256415:0.324028:0.256415:0.307473:0.232622:0.307473:0.000000:0.000000:0.000000
–:@0.339274:0.323372:0.348122:0.323372:0.348122:0.309696:0.339274:0.309696:0.000000
1:@0.348122:0.324023:0.356792:0.324023:0.356792:0.307468:0.348122:0.307468:0.000000
–:@0.480059:0.323372:0.488908:0.323372:0.488908:0.309696:0.480059:0.309696:0.000000
3/4:@0.488908:0.324023:0.512700:0.324023:0.512700:0.307468:0.488908:0.307468:0.000000:0.000000:0.000000
2:@0.158239:0.345365:0.166908:0.345365:0.166908:0.328809:0.158239:0.328809:0.000000
1:@0.240174:0.345365:0.248843:0.345365:0.248843:0.328809:0.240174:0.328809:0.000000
0:@0.343686:0.345365:0.352356:0.345365:0.352356:0.328809:0.343686:0.328809:0.000000
1:@0.492029:0.345365:0.500698:0.345365:0.500698:0.328809:0.492029:0.328809:0.000000
Recuerda que…:@0.684810:0.319452:0.794570:0.319452:0.794570:0.303980:0.684810:0.303980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las propiedades de la :@0.685048:0.348079:0.828456:0.348079:0.828456:0.333016:0.685048:0.333016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adición de funciones  son::@0.638505:0.363921:0.807051:0.363921:0.807051:0.348858:0.638505:0.348858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i.:@0.638505:0.395803:0.645453:0.395803:0.645453:0.380542:0.638505:0.380542:0.000000:0.000000
 :@0.645452:0.395605:0.649234:0.395605:0.649234:0.380542:0.645452:0.380542:0.000000
Conmutativa:@0.655127:0.396028:0.747860:0.396028:0.747860:0.380555:0.655127:0.380555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Para todo  :@0.747861:0.395605:0.825275:0.395605:0.825275:0.380542:0.747861:0.380542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.638505:0.411553:0.642287:0.411553:0.642287:0.396516:0.638505:0.396516:0.000000
f, g :@0.676446:0.411553:0.696798:0.411553:0.696798:0.396516:0.676446:0.396516:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.696798:0.411249:0.715848:0.411249:0.715848:0.397876:0.696798:0.397876:0.000000:0.000000
F(A), f + g = g + f.:@0.715848:0.411553:0.825345:0.411553:0.825345:0.396516:0.715848:0.396516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii. :@0.638504:0.443329:0.653070:0.443329:0.653070:0.428068:0.638504:0.428068:0.000000:0.000000:0.000000:0.000000
Asociativa:@0.655127:0.443554:0.728213:0.443554:0.728213:0.428081:0.655127:0.428081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Para todo  :@0.728213:0.443131:0.805627:0.443131:0.805627:0.428068:0.728213:0.428068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f, g, h    F(A),:@0.707211:0.459079:0.794563:0.459079:0.794563:0.444042:0.707211:0.444042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.746419:0.458775:0.761071:0.458775:0.761071:0.445402:0.746419:0.445402:0.000000
(f + g) + h = f + (g + h).:@0.676622:0.474921:0.825169:0.474921:0.825169:0.459884:0.676622:0.459884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iii. :@0.638504:0.506697:0.656956:0.506697:0.656956:0.491436:0.638504:0.491436:0.000000:0.000000:0.000000:0.000000:0.000000
Existencia de elemento :@0.655127:0.506922:0.819308:0.506922:0.819308:0.491449:0.655127:0.491449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
neutro:@0.655127:0.522764:0.702743:0.522764:0.702743:0.507291:0.655127:0.507291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Existe  :@0.702743:0.522341:0.753524:0.522341:0.753524:0.507278:0.702743:0.507278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f    F(A),:@0.753524:0.522447:0.814020:0.522447:0.814020:0.507410:0.753524:0.507410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o:@0.757521:0.525396:0.762095:0.525396:0.762095:0.516630:0.757521:0.516630:0.000000
:@0.765876:0.522143:0.780529:0.522143:0.780529:0.508770:0.765876:0.508770:0.000000
 tal :@0.814020:0.522341:0.838013:0.522341:0.838013:0.507278:0.814020:0.507278:0.000000:0.000000:0.000000:0.000000:0.000000
que para todo  :@0.655129:0.538183:0.755496:0.538183:0.755496:0.523120:0.655129:0.523120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f   F(A),:@0.755496:0.538289:0.811344:0.538289:0.811344:0.523252:0.755496:0.523252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.763201:0.537985:0.777853:0.537985:0.777853:0.524612:0.763201:0.524612:0.000000
f + f  = f  + f = f .:@0.698242:0.554131:0.803544:0.554131:0.803544:0.539094:0.698242:0.539094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o:@0.723668:0.557080:0.728241:0.557080:0.728241:0.548313:0.723668:0.548313:0.000000
o:@0.749736:0.557080:0.754310:0.557080:0.754310:0.548313:0.749736:0.548313:0.000000
iv. :@0.638514:0.585907:0.656122:0.585907:0.656122:0.570646:0.638514:0.570646:0.000000:0.000000:0.000000:0.000000
Existencia de opuestos :@0.655137:0.586132:0.816347:0.586132:0.816347:0.570659:0.655137:0.570659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aditivos :@0.655137:0.601974:0.716667:0.601974:0.716667:0.586501:0.655137:0.586501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Para cada :@0.710475:0.601551:0.782577:0.601551:0.782577:0.586488:0.710475:0.586488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f   F(A):@0.782577:0.601657:0.835821:0.601657:0.835821:0.586620:0.782577:0.586620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.790281:0.601353:0.804933:0.601353:0.804933:0.587980:0.790281:0.587980:0.000000
,  :@0.835821:0.601551:0.845901:0.601551:0.845901:0.586488:0.835821:0.586488:0.000000:0.000000:0.000000
existe :@0.655137:0.617393:0.695223:0.617393:0.695223:0.602330:0.655137:0.602330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   F(A),:@0.695223:0.617499:0.753938:0.617499:0.753938:0.602462:0.695223:0.602462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.705794:0.617195:0.720447:0.617195:0.720447:0.603822:0.705794:0.603822:0.000000
 tal que  :@0.753938:0.617393:0.810156:0.617393:0.810156:0.602330:0.753938:0.602330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f + g = f:@0.709711:0.635180:0.764078:0.635180:0.764078:0.618712:0.709711:0.618712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o:@0.764155:0.638410:0.769164:0.638410:0.769164:0.628809:0.764155:0.628809:0.000000
 . :@0.769164:0.634744:0.779243:0.634744:0.779243:0.619681:0.769164:0.619681:0.000000:0.000000:0.000000
  Esta función g se denota – ,:@0.638505:0.664923:0.834708:0.664919:0.834708:0.649856:0.638505:0.649860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.827896:0.665356:0.832192:0.665356:0.832192:0.648887:0.827896:0.648887:0.000000
 :@0.638508:0.682266:0.642290:0.682266:0.642290:0.667203:0.638508:0.667203:0.000000
así,    = – .:@0.716978:0.682266:0.784810:0.682270:0.784810:0.667207:0.716978:0.667203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.743544:0.682706:0.750981:0.682706:0.750981:0.666238:0.743544:0.666238:0.000000
f:@0.777997:0.682706:0.782293:0.682706:0.782293:0.666238:0.777997:0.666238:0.000000
  Para cada :@0.638513:0.714192:0.721045:0.714192:0.721045:0.699129:0.638513:0.699129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x A, f(x):@0.724390:0.715064:0.800881:0.715064:0.800881:0.697849:0.724390:0.697849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.736009:0.715637:0.750342:0.715637:0.750342:0.695978:0.736009:0.695978:0.000000
∈:@0.803776:0.715637:0.818109:0.715637:0.818109:0.695978:0.803776:0.695978:0.000000
!:@0.817908:0.715939:0.832422:0.715939:0.832422:0.697668:0.817908:0.697668:0.000000
,:@0.834131:0.715064:0.837006:0.715064:0.837006:0.697849:0.834131:0.697849:0.000000
 :@0.839981:0.714193:0.843763:0.714193:0.843763:0.699130:0.839981:0.699130:0.000000
luego :@0.655128:0.730035:0.694828:0.730035:0.694828:0.714972:0.655128:0.714972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.697762:0.731760:0.708798:0.731760:0.708798:0.712101:0.697762:0.712101:0.000000
f(x):@0.709803:0.731187:0.737465:0.731187:0.737465:0.713972:0.709803:0.713972:0.000000:0.000000:0.000000:0.000000
∈:@0.740360:0.731760:0.754693:0.731760:0.754693:0.712101:0.740360:0.712101:0.000000
!:@0.754492:0.732062:0.769006:0.732062:0.769006:0.713791:0.754492:0.713791:0.000000
 es tal que :@0.773566:0.730035:0.842904:0.730035:0.842904:0.714972:0.773566:0.714972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) + (–f(x)) = 0. Se define la :@0.655133:0.745877:0.847214:0.745877:0.847214:0.730814:0.655133:0.730814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función –f como :@0.655133:0.761719:0.768747:0.761719:0.768747:0.746656:0.655133:0.746656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  (-f)(x) = –f(x), :@0.638510:0.777561:0.750084:0.777561:0.750084:0.762498:0.638510:0.762498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀ ∈:@0.753011:0.778615:0.793197:0.778615:0.793197:0.758956:0.753011:0.758956:0.000000:0.000000:0.000000
x A.:@0.767244:0.778042:0.809158:0.778042:0.809158:0.760827:0.767244:0.760827:0.000000:0.000000:0.000000:0.000000
  Se tiene f + (–f) = f .:@0.638510:0.793403:0.786123:0.793403:0.786123:0.778340:0.638510:0.778340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.779084:0.796396:0.783607:0.796396:0.783607:0.787614:0.779084:0.787614:0.000000
y = f(x) + g(x):@0.675746:0.193424:0.709181:0.193424:0.709181:0.187775:0.675746:0.187775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y =      x:@0.683531:0.116201:0.702724:0.116201:0.702724:0.110553:0.683531:0.110553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.702722:0.114012:0.704396:0.114012:0.704396:0.110719:0.702722:0.110719:0.000000
1:@0.694064:0.114146:0.696435:0.114146:0.696435:0.109484:0.694064:0.109484:0.000000
4:@0.694064:0.118126:0.696435:0.118126:0.696435:0.113463:0.694064:0.113463:0.000000
y = x – 2:@0.824544:0.140334:0.845702:0.140334:0.845702:0.134686:0.824544:0.134686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.739575:0.116924:0.742447:0.116924:0.742447:0.111275:0.739575:0.111275:0.000000
2:@0.739575:0.132248:0.742447:0.132248:0.742447:0.126600:0.739575:0.126600:0.000000
1:@0.739575:0.147573:0.742447:0.147573:0.742447:0.141925:0.739575:0.141925:0.000000
0:@0.741468:0.165569:0.744340:0.165569:0.744340:0.159921:0.741468:0.159921:0.000000
–1:@0.737851:0.178223:0.744171:0.178223:0.744171:0.172574:0.737851:0.172574:0.000000:0.000000
–2:@0.750096:0.193547:0.756416:0.193547:0.756416:0.187899:0.750096:0.187899:0.000000:0.000000
–3:@0.750096:0.208872:0.756416:0.208872:0.756416:0.203224:0.750096:0.203224:0.000000:0.000000
–4:@0.750096:0.224197:0.756416:0.224197:0.756416:0.218549:0.750096:0.218549:0.000000:0.000000
–5:@0.750096:0.239522:0.756416:0.239522:0.756416:0.233873:0.750096:0.233873:0.000000:0.000000
–4:@0.661563:0.168099:0.667883:0.168099:0.667883:0.162450:0.661563:0.162450:0.000000:0.000000
–3:@0.681981:0.168099:0.688302:0.168099:0.688302:0.162450:0.681981:0.162450:0.000000:0.000000
–2:@0.702400:0.168099:0.708720:0.168099:0.708720:0.162450:0.702400:0.162450:0.000000:0.000000
–1:@0.722819:0.168099:0.729139:0.168099:0.729139:0.162450:0.722819:0.162450:0.000000:0.000000
1:@0.765374:0.168099:0.768246:0.168099:0.768246:0.162450:0.765374:0.162450:0.000000
2:@0.785793:0.168099:0.788665:0.168099:0.788665:0.162450:0.785793:0.162450:0.000000
3:@0.806212:0.168099:0.809084:0.168099:0.809084:0.162450:0.806212:0.162450:0.000000
4:@0.826631:0.168099:0.829503:0.168099:0.829503:0.162450:0.826631:0.162450:0.000000
x:@0.847179:0.165578:0.849792:0.165578:0.849792:0.159930:0.847179:0.159930:0.000000
y:@0.739679:0.094944:0.742376:0.094944:0.742376:0.089295:0.739679:0.089295:0.000000
p:@0.792835:0.274479:0.804315:0.274479:0.804315:0.264454:0.792835:0.264454:0.000000
 :@0.804315:0.275187:0.807197:0.275187:0.807197:0.263710:0.804315:0.263710:0.000000
Figura 2.2.:@0.807197:0.275187:0.855765:0.275187:0.855765:0.263710:0.807197:0.263710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.684810:0.842108:0.752276:0.842108:0.752276:0.824425:0.684810:0.824425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
argumento::@0.685048:0.868921:0.761283:0.868921:0.761283:0.853660:0.685048:0.853660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 razonamien-:@0.761107:0.868723:0.844783:0.868723:0.844783:0.853660:0.761107:0.853660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to para probar o demostrar una :@0.638505:0.884565:0.842985:0.884565:0.842985:0.869502:0.638505:0.869502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proposición, o para convencer :@0.638505:0.900407:0.833524:0.900407:0.833524:0.885344:0.638505:0.885344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de lo que se afirma o se niega.:@0.638505:0.916249:0.827223:0.916249:0.827223:0.901186:0.638505:0.901186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.632075:0.845841:0.643479:0.844331:0.638277:0.822186:0.626872:0.823696:0.000000
c:@0.635456:0.856810:0.646056:0.855407:0.640973:0.833772:0.630374:0.835175:0.000000
b:@0.645832:0.849592:0.658545:0.847909:0.653414:0.826067:0.640700:0.827749:0.000000
 ©:@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