188:@0.026565:0.967627:0.050760:0.967627:0.050760:0.951847:0.026565:0.951847:0.000000:0.000000:0.000000
Idea intuitiva de límite:@0.404235:0.100847:0.692811:0.100847:0.692811:0.056188:0.404235:0.056188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.32. Calcular, de manera intuitiva, el límite cuando h 0 de una función cuadrática con el uso de la calculadora como una distancia entre dos número reales.:@0.143847:0.954873:0.839445:0.954873:0.839445:0.944831:0.143847:0.944831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.388548:0.956466:0.400122:0.956466:0.400122:0.944998:0.388548:0.944998:0.000000
De manera intuitiva, las ideas de proximidad, de tendencia, de aproxi-:@0.404236:0.141121:0.891817:0.141121:0.891817:0.124624:0.404236:0.124624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mación y de cercanía a un punto, a un valor numérico o también de :@0.404236:0.158472:0.895961:0.158472:0.895961:0.141974:0.404236:0.141974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tendencia a alejarse, están ligadas con la distancia entre dos puntos en :@0.404236:0.175823:0.895922:0.175823:0.895922:0.159325:0.404236:0.159325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la recta numérica, a la cual definimos a continuación.:@0.404236:0.193174:0.780194:0.193174:0.780194:0.176676:0.404236:0.176676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404236:0.210524:0.408378:0.210524:0.408378:0.194027:0.404236:0.194027:0.000000
Definición :@0.404236:0.228338:0.491103:0.228338:0.491103:0.211392:0.404236:0.211392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean x, y :@0.484322:0.227875:0.556740:0.227875:0.556740:0.211377:0.484322:0.211377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.569403:0.227658:0.574219:0.227658:0.574219:0.213011:0.569403:0.213011:0.000000
R:@0.574414:0.226670:0.587114:0.226670:0.587114:0.214392:0.574414:0.214392:0.000000
. La distancia de  a  se denota :@0.587114:0.227875:0.813825:0.227875:0.813825:0.211377:0.587114:0.211377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x  y :@0.703823:0.227991:0.739560:0.227991:0.739560:0.211522:0.703823:0.211522:0.000000:0.000000:0.000000:0.000000:0.000000
d (x, y) :@0.813999:0.227991:0.864936:0.227991:0.864936:0.211522:0.813999:0.211522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y se :@0.865110:0.227875:0.895953:0.227875:0.895953:0.211377:0.865110:0.211377:0.000000:0.000000:0.000000:0.000000:0.000000
define como :@0.404248:0.245226:0.499012:0.245226:0.499012:0.228728:0.404248:0.228728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d (x, y) =  x – y:@0.592084:0.262692:0.696194:0.262692:0.696194:0.246224:0.592084:0.246224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
|:@0.657702:0.262577:0.662711:0.262577:0.662711:0.246079:0.657702:0.246079:0.000000
|.:@0.696194:0.262577:0.703958:0.262577:0.703958:0.246079:0.696194:0.246079:0.000000:0.000000
De la definición de valor absoluto y de la distancia entre dos números :@0.404248:0.289991:0.895969:0.289991:0.895969:0.273493:0.404248:0.273493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales, se tiene::@0.404248:0.307342:0.507912:0.307342:0.507912:0.290844:0.404248:0.290844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i i:@0.426684:0.327695:0.446651:0.325458:0.446651:0.308465:0.426684:0.310702:0.000000:0.000000:0.000000
) ):@0.431114:0.331362:0.453784:0.329125:0.453784:0.306951:0.431114:0.309187:0.000000:0.000000:0.000000
ii ii:@0.426684:0.360371:0.450368:0.358134:0.450368:0.341141:0.426684:0.343378:0.000000:0.000000:0.000000:0.000000:0.000000
) ):@0.434841:0.364039:0.457511:0.361803:0.457511:0.339628:0.434841:0.341865:0.000000:0.000000:0.000000
d x y x y:@0.426684:0.394629:0.482645:0.392393:0.482645:0.375400:0.426684:0.377636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( , ) , ):@0.436524:0.394509:0.489006:0.392274:0.489006:0.375251:0.436524:0.377486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, ,:@0.523810:0.394509:0.542705:0.392274:0.542705:0.375251:0.523810:0.377486:0.000000:0.000000:0.000000
, ,:@0.523810:0.424676:0.542703:0.422440:0.542703:0.405417:0.523810:0.407653:0.000000:0.000000:0.000000
= =:@0.475779:0.395166:0.502742:0.392930:0.502742:0.376131:0.475779:0.378367:0.000000:0.000000:0.000000
x y x y:@0.490529:0.394629:0.539419:0.392393:0.539419:0.375400:0.490529:0.377636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– –:@0.501124:0.394509:0.528008:0.392274:0.528008:0.375251:0.501124:0.377486:0.000000:0.000000:0.000000
d x y x y:@0.426678:0.424796:0.482646:0.422560:0.482646:0.405567:0.426678:0.407803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( , ) , ):@0.436518:0.424676:0.489007:0.422440:0.489007:0.405417:0.436518:0.407653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= =:@0.475779:0.425333:0.502744:0.423097:0.502744:0.406298:0.475779:0.408534:0.000000:0.000000:0.000000
y x y x:@0.490966:0.424796:0.539201:0.422560:0.539201:0.405567:0.490966:0.407803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– –:@0.501561:0.424676:0.528447:0.422440:0.528447:0.405417:0.501561:0.407653:0.000000:0.000000:0.000000
si  ≥ entonces :@0.444795:0.328327:0.568939:0.328327:0.568939:0.311830:0.444795:0.311830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x   y, :@0.458994:0.328443:0.500087:0.328443:0.500087:0.311974:0.458994:0.311974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x – y   0:@0.568939:0.328443:0.629586:0.328443:0.629586:0.311974:0.568939:0.311974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≥ , luego, :@0.606564:0.328327:0.682525:0.328327:0.682525:0.311830:0.606564:0.311830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d (x, y) = |x – y| = x – y,  :@0.682525:0.328443:0.854930:0.328443:0.854930:0.311974:0.682525:0.311974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y.:@0.854930:0.328327:0.864736:0.328327:0.864736:0.311830:0.854930:0.311830:0.000000:0.000000
si  < entonces :@0.449824:0.359747:0.573967:0.359747:0.573967:0.343249:0.449824:0.343249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x   y, :@0.464022:0.359862:0.505115:0.359862:0.505115:0.343393:0.464022:0.343393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y – x   0:@0.573967:0.359862:0.634614:0.359862:0.634614:0.343393:0.573967:0.343393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
> , resulta, :@0.611592:0.359747:0.696068:0.359747:0.696068:0.343249:0.611592:0.343249:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d (x, y) =  x – y  = y – x.:@0.696068:0.359862:0.860804:0.359862:0.860804:0.343393:0.696068:0.343393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
|:@0.761686:0.359747:0.766695:0.359747:0.766695:0.343249:0.761686:0.343249:0.000000
|:@0.800178:0.359747:0.805187:0.359747:0.805187:0.343249:0.800178:0.343249:0.000000
Así, :@0.404242:0.405234:0.433352:0.405234:0.433352:0.388737:0.404242:0.388737:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.442735:0.392393:0.452197:0.392393:0.452197:0.375400:0.442735:0.375400:0.000000
(:@0.452575:0.392274:0.458717:0.392274:0.458717:0.375251:0.452575:0.375251:0.000000
d:@0.442730:0.422560:0.452192:0.422560:0.452192:0.405567:0.442730:0.405567:0.000000
(:@0.452570:0.422440:0.458712:0.422440:0.458712:0.405417:0.452570:0.405417:0.000000
si  ≥:@0.551548:0.392748:0.588172:0.392748:0.588172:0.376250:0.551548:0.376250:0.000000:0.000000:0.000000:0.000000:0.000000
x   y,:@0.565747:0.392863:0.602698:0.392863:0.602698:0.376394:0.565747:0.376394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si  <:@0.551548:0.421622:0.588172:0.421622:0.588172:0.405124:0.551548:0.405124:0.000000:0.000000:0.000000:0.000000:0.000000
x   y.:@0.565747:0.421738:0.602698:0.421738:0.602698:0.405269:0.565747:0.405269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A la distancia entre dos números reales la denominaremos :@0.404227:0.447055:0.830871:0.447055:0.830871:0.430558:0.404227:0.430558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
métrica :@0.832047:0.447518:0.895718:0.447518:0.895718:0.430572:0.832047:0.430572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
usual en:@0.404227:0.464869:0.469960:0.464869:0.469960:0.447923:0.404227:0.447923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   y, como se dijo, esta nos permite medir la proximidad :@0.469960:0.464406:0.895912:0.464410:0.895912:0.447912:0.469960:0.447908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.476060:0.463205:0.488760:0.463205:0.488760:0.450927:0.476060:0.450927:0.000000
 :@0.891770:0.464410:0.895912:0.464410:0.895912:0.447912:0.891770:0.447912:0.000000
o lejanía entre dos números reales.:@0.404244:0.481761:0.647256:0.481761:0.647256:0.465263:0.404244:0.465263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.404244:0.516925:0.549196:0.516925:0.549196:0.499979:0.404244:0.499979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.404244:0.534030:0.420600:0.534030:0.420600:0.517315:0.404244:0.517315:0.000000:0.000000:0.000000
  Para  = –3, :@0.420600:0.533813:0.514923:0.533813:0.514923:0.517315:0.420600:0.517315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.462463:0.533929:0.474080:0.533929:0.474080:0.517460:0.462463:0.517460:0.000000:0.000000
y =  , :@0.514923:0.533929:0.557268:0.533929:0.557268:0.517460:0.514923:0.517460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 se tiene  (–3, 1)  | 3 –1| = |–4| = 4.:@0.541778:0.533813:0.828732:0.533813:0.828732:0.517315:0.541778:0.517315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d :@0.615678:0.533929:0.628990:0.533929:0.628990:0.517460:0.615678:0.517460:0.000000:0.000000
 =  –:@0.675285:0.533929:0.713642:0.533929:0.713642:0.517460:0.675285:0.517460:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.404244:0.551381:0.420600:0.551381:0.420600:0.534666:0.404244:0.534666:0.000000:0.000000:0.000000
  Si  = 4,6 =   entonces  (4,6; 4,6)  |4,6 – 4,6| = 0.:@0.420600:0.551164:0.786272:0.551164:0.786272:0.534666:0.420600:0.534666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.443930:0.551279:0.455547:0.551279:0.455547:0.534811:0.443930:0.534811:0.000000:0.000000
y,:@0.509336:0.551279:0.519720:0.551279:0.519720:0.534811:0.509336:0.534811:0.000000:0.000000
d :@0.592714:0.551279:0.606026:0.551279:0.606026:0.534811:0.592714:0.534811:0.000000:0.000000
 = :@0.664323:0.551279:0.683492:0.551279:0.683492:0.534811:0.664323:0.534811:0.000000:0.000000:0.000000
3.:@0.404244:0.568731:0.416516:0.568731:0.416516:0.552017:0.404244:0.552017:0.000000:0.000000
    (–8, –2) = | 8 –(–2)| = | 8 + 2| = | 6| = 6.:@0.416516:0.568514:0.744487:0.568514:0.744487:0.552017:0.416516:0.552017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.427979:0.568630:0.437149:0.568630:0.437149:0.552161:0.427979:0.552161:0.000000
–:@0.522186:0.568630:0.532223:0.568630:0.532223:0.552161:0.522186:0.552161:0.000000
–:@0.615372:0.568630:0.625409:0.568630:0.625409:0.552161:0.615372:0.552161:0.000000
–:@0.690602:0.568630:0.700640:0.568630:0.700640:0.552161:0.690602:0.552161:0.000000
Propiedades de la métrica usual en :@0.404236:0.604613:0.687238:0.604613:0.687238:0.586931:0.404236:0.586931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.687238:0.603120:0.701753:0.603120:0.701753:0.589088:0.687238:0.589088:0.000000
Teorema :@0.404236:0.621784:0.477964:0.621784:0.477964:0.604838:0.404236:0.604838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean :@0.471183:0.621321:0.515763:0.621321:0.515763:0.604823:0.471183:0.604823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x, y, z :@0.515763:0.621437:0.555661:0.621437:0.555661:0.604968:0.515763:0.604968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.568158:0.621104:0.572975:0.621104:0.572975:0.606457:0.568158:0.606457:0.000000
R:@0.572975:0.620116:0.585675:0.620116:0.585675:0.607838:0.572975:0.607838:0.000000
. Se verifican las siguientes propiedades.:@0.585675:0.621321:0.864264:0.621321:0.864264:0.604823:0.585675:0.604823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i)  :@0.404235:0.638889:0.422941:0.638889:0.422941:0.622174:0.404235:0.622174:0.000000:0.000000:0.000000:0.000000
  (:@0.422941:0.638672:0.443093:0.638672:0.443093:0.622174:0.422941:0.622174:0.000000:0.000000:0.000000
d x, y:@0.427969:0.638787:0.465363:0.638787:0.465363:0.622319:0.427969:0.622319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) ≥ 0.:@0.465363:0.638672:0.501659:0.638672:0.501659:0.622174:0.465363:0.622174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.486266:0.638787:0.490408:0.638787:0.490408:0.622319:0.486266:0.622319:0.000000
ii):@0.404235:0.656239:0.419030:0.656239:0.419030:0.639525:0.404235:0.639525:0.000000:0.000000:0.000000
  (:@0.419030:0.656023:0.443093:0.656023:0.443093:0.639525:0.419030:0.639525:0.000000:0.000000:0.000000
d x, y:@0.427969:0.656138:0.465363:0.656138:0.465363:0.639669:0.427969:0.639669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) = 0:@0.465363:0.656023:0.498904:0.656023:0.498904:0.639525:0.465363:0.639525:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.498904:0.656138:0.503046:0.656138:0.503046:0.639669:0.498904:0.639669:0.000000
⇔ :@0.503046:0.656572:0.527937:0.656572:0.527937:0.637732:0.503046:0.637732:0.000000:0.000000
x :@0.527937:0.656138:0.539554:0.656138:0.539554:0.639669:0.527937:0.639669:0.000000:0.000000
= y.:@0.539554:0.656023:0.564310:0.656023:0.564310:0.639525:0.539554:0.639525:0.000000:0.000000:0.000000:0.000000
iii):@0.404235:0.673590:0.423288:0.673590:0.423288:0.656876:0.404235:0.656876:0.000000:0.000000:0.000000:0.000000
   (:@0.423288:0.673373:0.443093:0.673373:0.443093:0.656876:0.423288:0.656876:0.000000:0.000000:0.000000:0.000000
d x, y:@0.427969:0.673489:0.465363:0.673489:0.465363:0.657020:0.427969:0.657020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) ≥:@0.465363:0.673373:0.486266:0.673373:0.486266:0.656876:0.465363:0.656876:0.000000:0.000000:0.000000
 d (y, x):@0.486266:0.673489:0.536587:0.673489:0.536587:0.657020:0.486266:0.657020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.536587:0.673373:0.543484:0.673373:0.543484:0.656876:0.536587:0.656876:0.000000:0.000000
iv) :@0.404235:0.690941:0.427122:0.690941:0.427122:0.674226:0.404235:0.674226:0.000000:0.000000:0.000000:0.000000
  (:@0.427122:0.690724:0.443093:0.690724:0.443093:0.674226:0.427122:0.674226:0.000000:0.000000:0.000000
d x, z:@0.427969:0.690840:0.464323:0.690840:0.464323:0.674371:0.427969:0.674371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) ≤ (:@0.464323:0.690724:0.508633:0.690724:0.508633:0.674226:0.464323:0.674226:0.000000:0.000000:0.000000:0.000000:0.000000
 d  x, y:@0.485226:0.690840:0.530904:0.690840:0.530904:0.674371:0.485226:0.674371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) +  ( ) (desigualdad triangular). :@0.530904:0.690724:0.777844:0.690724:0.777844:0.674226:0.530904:0.674226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  y,z:@0.555948:0.690840:0.592244:0.690840:0.592244:0.674371:0.555948:0.674371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Demostración :@0.404235:0.717343:0.520308:0.717343:0.520308:0.700397:0.404235:0.700397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Estas propiedades resultan inmediatamente de las :@0.513526:0.716880:0.895938:0.716880:0.895938:0.700383:0.513526:0.700383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades del valor absoluto.:@0.404235:0.734231:0.626380:0.734231:0.626380:0.717733:0.404235:0.717733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i) :@0.404235:0.751799:0.418857:0.751799:0.418857:0.735084:0.404235:0.735084:0.000000:0.000000:0.000000
  Puesto que |:@0.418857:0.751582:0.516378:0.751582:0.516378:0.735084:0.418857:0.735084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x – y:@0.516378:0.751698:0.549861:0.751698:0.549861:0.735229:0.516378:0.735229:0.000000:0.000000:0.000000:0.000000:0.000000
| ≥ 0, se sigue que   (:@0.549861:0.751582:0.702613:0.751582:0.702613:0.735084:0.549861:0.735084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  x, y:@0.683348:0.751698:0.724883:0.751698:0.724883:0.735229:0.683348:0.735229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) = |:@0.724883:0.751582:0.754937:0.751582:0.754937:0.735084:0.724883:0.735084:0.000000:0.000000:0.000000:0.000000:0.000000
x – y:@0.754937:0.751698:0.788420:0.751698:0.788420:0.735229:0.754937:0.735229:0.000000:0.000000:0.000000:0.000000:0.000000
| ≥ 0.:@0.788420:0.751582:0.823772:0.751582:0.823772:0.735084:0.788420:0.735084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.808379:0.751698:0.812521:0.751698:0.812521:0.735229:0.808379:0.735229:0.000000
ii) :@0.404235:0.769149:0.423114:0.769149:0.423114:0.752435:0.404235:0.752435:0.000000:0.000000:0.000000:0.000000
 De la definición de distancia entre dos números reales, se tiene  :@0.423114:0.768933:0.895903:0.768933:0.895903:0.752435:0.423114:0.752435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891755:0.768933:0.895897:0.768933:0.895897:0.752435:0.891755:0.752435:0.000000
 :@0.891755:0.768933:0.895897:0.768933:0.895897:0.752435:0.891755:0.752435:0.000000
 :@0.891755:0.768933:0.895897:0.768933:0.895897:0.752435:0.891755:0.752435:0.000000
d x, y:@0.427969:0.786399:0.465363:0.786399:0.465363:0.769930:0.427969:0.769930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.437140:0.786283:0.443093:0.786283:0.443093:0.769786:0.437140:0.769786:0.000000
) = |:@0.465363:0.786283:0.495417:0.786283:0.495417:0.769786:0.465363:0.769786:0.000000:0.000000:0.000000:0.000000:0.000000
x – y:@0.495417:0.786399:0.528900:0.786399:0.528900:0.769930:0.495417:0.769930:0.000000:0.000000:0.000000:0.000000:0.000000
|, luego,:@0.528900:0.786283:0.582706:0.786283:0.582706:0.769786:0.528900:0.769786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404235:0.803634:0.408377:0.803634:0.408377:0.787136:0.404235:0.787136:0.000000
d x, y:@0.427969:0.803750:0.465363:0.803750:0.465363:0.787281:0.427969:0.787281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.437140:0.803634:0.443093:0.803634:0.443093:0.787136:0.437140:0.787136:0.000000
) = 0 :@0.465363:0.803634:0.503046:0.803634:0.503046:0.787136:0.465363:0.787136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⇔:@0.503046:0.804184:0.523120:0.804184:0.523120:0.785344:0.503046:0.785344:0.000000
 |:@0.523120:0.803634:0.532271:0.803634:0.532271:0.787136:0.523120:0.787136:0.000000:0.000000
x – y:@0.532271:0.803750:0.565754:0.803750:0.565754:0.787281:0.532271:0.787281:0.000000:0.000000:0.000000:0.000000:0.000000
| = 0 :@0.565754:0.803634:0.602493:0.803634:0.602493:0.787136:0.565754:0.787136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⇔:@0.602493:0.804184:0.622568:0.804184:0.622568:0.785344:0.602493:0.785344:0.000000
 :@0.622568:0.803634:0.626710:0.803634:0.626710:0.787136:0.622568:0.787136:0.000000
x – y = :@0.626710:0.803750:0.679362:0.803750:0.679362:0.787281:0.626710:0.787281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 :@0.679362:0.803634:0.692000:0.803634:0.692000:0.787136:0.679362:0.787136:0.000000:0.000000
⇔:@0.692000:0.804184:0.712074:0.804184:0.712074:0.785344:0.692000:0.785344:0.000000
 :@0.712074:0.803634:0.716216:0.803634:0.716216:0.787136:0.712074:0.787136:0.000000
x = y.:@0.716216:0.803750:0.753244:0.803750:0.753244:0.787281:0.716216:0.787281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   Por lo tanto,  (:@0.404235:0.820985:0.538706:0.820985:0.538706:0.804487:0.404235:0.804487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  x, y:@0.519441:0.821101:0.560977:0.821101:0.560977:0.804632:0.519441:0.804632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) =  0 :@0.560977:0.820985:0.602802:0.820985:0.602802:0.804487:0.560977:0.804487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⇔:@0.602802:0.821534:0.622876:0.821534:0.622876:0.802694:0.602802:0.802694:0.000000
 :@0.622876:0.820985:0.627018:0.820985:0.627018:0.804487:0.622876:0.804487:0.000000
x = y:@0.627018:0.821101:0.661349:0.821101:0.661349:0.804632:0.627018:0.804632:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.661349:0.820985:0.664104:0.820985:0.664104:0.804487:0.661349:0.804487:0.000000
iii):@0.404235:0.838552:0.423288:0.838552:0.423288:0.821838:0.404235:0.821838:0.000000:0.000000:0.000000:0.000000
 :@0.423288:0.838798:0.427314:0.838798:0.427314:0.821852:0.423288:0.821852:0.000000
Tenemos  (:@0.427314:0.838336:0.511253:0.838336:0.511253:0.821838:0.427314:0.821838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d x, y:@0.496130:0.838451:0.533524:0.838451:0.533524:0.821983:0.496130:0.821983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) = |  1(:@0.533524:0.838336:0.592206:0.838336:0.592206:0.821838:0.533524:0.821838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– y – x:@0.563577:0.838451:0.625689:0.838451:0.625689:0.821983:0.563577:0.821983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
)| = |–1||:@0.625689:0.838336:0.689765:0.838336:0.689765:0.821838:0.625689:0.821838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y – x:@0.689765:0.838451:0.723248:0.838451:0.723248:0.821983:0.689765:0.821983:0.000000:0.000000:0.000000:0.000000:0.000000
| =  (:@0.723248:0.838336:0.762472:0.838336:0.762472:0.821838:0.723248:0.821838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d y, x .  :@0.747349:0.838451:0.801561:0.838451:0.801561:0.821983:0.747349:0.821983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) Así,:@0.784473:0.838336:0.826529:0.838336:0.826529:0.821838:0.784473:0.821838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404235:0.855686:0.408377:0.855686:0.408377:0.839189:0.404235:0.839189:0.000000
d  x, y:@0.427969:0.855802:0.469505:0.855802:0.469505:0.839333:0.427969:0.839333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.441282:0.855686:0.447235:0.855686:0.447235:0.839189:0.441282:0.839189:0.000000
) =   (:@0.469505:0.855686:0.517957:0.855686:0.517957:0.839189:0.469505:0.839189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  y, x:@0.498692:0.855802:0.539958:0.855802:0.539958:0.839333:0.498692:0.839333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
).:@0.539958:0.855686:0.548666:0.855686:0.548666:0.839189:0.539958:0.839189:0.000000:0.000000
iv):@0.404235:0.873254:0.423037:0.873254:0.423037:0.856539:0.404235:0.856539:0.000000:0.000000:0.000000
 :@0.423037:0.873500:0.427064:0.873500:0.427064:0.856554:0.423037:0.856554:0.000000
 Por la desigualdad triangular del valor absoluto, se tiene:@0.427064:0.873037:0.820724:0.873037:0.820724:0.856539:0.427064:0.856539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
      (:@0.404235:0.890388:0.443093:0.890388:0.443093:0.873890:0.404235:0.873890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d x, y:@0.427969:0.890504:0.465363:0.890504:0.465363:0.874035:0.427969:0.874035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) = |:@0.465363:0.890388:0.495417:0.890388:0.495417:0.873890:0.465363:0.873890:0.000000:0.000000:0.000000:0.000000:0.000000
x – y d(y, z):@0.495417:0.890504:0.586156:0.890504:0.586156:0.874035:0.495417:0.874035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
|,  :@0.528900:0.890388:0.544948:0.890388:0.544948:0.873890:0.528900:0.873890:0.000000:0.000000:0.000000:0.000000
 = |:@0.586156:0.890388:0.610257:0.890388:0.610257:0.873890:0.586156:0.873890:0.000000:0.000000:0.000000:0.000000
y – z:@0.610257:0.890504:0.642912:0.890504:0.642912:0.874035:0.610257:0.874035:0.000000:0.000000:0.000000:0.000000:0.000000
|.  Luego,:@0.642912:0.890388:0.704927:0.890388:0.704927:0.873890:0.642912:0.873890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404235:0.907739:0.408377:0.907739:0.408377:0.891241:0.404235:0.891241:0.000000
d x, z:@0.427969:0.907854:0.464323:0.907854:0.464323:0.891386:0.427969:0.891386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.437140:0.907739:0.443093:0.907739:0.443093:0.891241:0.437140:0.891241:0.000000
) = |:@0.464323:0.907739:0.494377:0.907739:0.494377:0.891241:0.464323:0.891241:0.000000:0.000000:0.000000:0.000000:0.000000
x – z:@0.494377:0.907854:0.526819:0.907854:0.526819:0.891386:0.494377:0.891386:0.000000:0.000000:0.000000:0.000000:0.000000
|=|:@0.526819:0.907739:0.547645:0.907739:0.547645:0.891241:0.526819:0.891241:0.000000:0.000000:0.000000
x – y + y – z:@0.547645:0.907854:0.632952:0.907854:0.632952:0.891386:0.547645:0.891386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| ≤ |:@0.632952:0.907739:0.662061:0.907739:0.662061:0.891241:0.632952:0.891241:0.000000:0.000000:0.000000:0.000000:0.000000
x – y:@0.662061:0.907854:0.695544:0.907854:0.695544:0.891386:0.662061:0.891386:0.000000:0.000000:0.000000:0.000000:0.000000
|+|:@0.695544:0.907739:0.716370:0.907739:0.716370:0.891241:0.695544:0.891241:0.000000:0.000000:0.000000
y – z:@0.716370:0.907854:0.749025:0.907854:0.749025:0.891386:0.716370:0.891386:0.000000:0.000000:0.000000:0.000000:0.000000
| =  (:@0.749025:0.907739:0.788133:0.907739:0.788133:0.891241:0.749025:0.891241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.754034:0.908201:0.758060:0.908201:0.758060:0.891255:0.754034:0.891255:0.000000
d x, y:@0.773010:0.907854:0.810404:0.907854:0.810404:0.891386:0.773010:0.891386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) +  (:@0.810404:0.907739:0.850456:0.907739:0.850456:0.891241:0.810404:0.891241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.816357:0.908201:0.820383:0.908201:0.820383:0.891255:0.816357:0.891255:0.000000
d y, z:@0.835333:0.907854:0.871629:0.907854:0.871629:0.891386:0.835333:0.891386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
).:@0.871610:0.907739:0.880318:0.907739:0.880318:0.891241:0.871610:0.891241:0.000000:0.000000
 :@0.880318:0.908201:0.884344:0.908201:0.884344:0.891255:0.880318:0.891255:0.000000
Conclusión :@0.404215:0.925552:0.497478:0.925552:0.497478:0.908606:0.404215:0.908606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: (:@0.490697:0.925089:0.512602:0.925089:0.512602:0.908592:0.490697:0.908592:0.000000:0.000000:0.000000
d x, z:@0.497478:0.925205:0.533832:0.925205:0.533832:0.908736:0.497478:0.908736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) ≤  (:@0.533832:0.925089:0.574000:0.925089:0.574000:0.908592:0.533832:0.908592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d x, y:@0.558877:0.925205:0.596271:0.925205:0.596271:0.908736:0.558877:0.908736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) +  (:@0.596271:0.925089:0.636439:0.925089:0.636439:0.908592:0.596271:0.908592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d y, z:@0.621315:0.925205:0.657611:0.925205:0.657611:0.908736:0.621315:0.908736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
). :@0.657611:0.925089:0.670461:0.925089:0.670461:0.908592:0.657611:0.908592:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.221370:0.363493:0.221370:0.363493:0.205897:0.199646:0.205897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo se define la :@0.199884:0.249997:0.326090:0.249997:0.326090:0.234934:0.199884:0.234934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
distancia entre dos números :@0.153341:0.265839:0.340393:0.265839:0.340393:0.250776:0.153341:0.250776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales?:@0.153341:0.281681:0.194607:0.281681:0.194607:0.266618:0.153341:0.266618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.095593:0.307805:0.095593:0.307805:0.080121:0.199646:0.080121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo se define el valor :@0.199884:0.124221:0.361990:0.124221:0.361990:0.109158:0.199884:0.109158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
absoluto de un número real? :@0.153341:0.140063:0.342959:0.140063:0.342959:0.125000:0.153341:0.125000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuáles son las propiedades :@0.153341:0.155905:0.336662:0.155905:0.336662:0.140842:0.153341:0.140842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
más importantes? :@0.153341:0.171747:0.273004:0.171747:0.273004:0.156684:0.153341:0.156684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Distancia entre dos números reales:@0.404235:0.119171:0.684262:0.119171:0.684262:0.101488:0.404235:0.101488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.200180:0.394509:0.297803:0.394509:0.297803:0.379037:0.200180:0.379037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.200180:0.407077:0.284243:0.407077:0.284243:0.391605:0.200180:0.391605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si  =  – :@0.200418:0.431552:0.259521:0.431552:0.259521:0.416488:0.200418:0.416488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u  x  y, v  y – z:@0.213400:0.431657:0.320804:0.431657:0.320804:0.416621:0.213400:0.416621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= :@0.280505:0.431552:0.293628:0.431552:0.293628:0.416488:0.280505:0.416488:0.000000:0.000000
, se :@0.320277:0.431552:0.342071:0.431552:0.342071:0.416488:0.320277:0.416488:0.000000:0.000000:0.000000:0.000000:0.000000
tiene :@0.153875:0.447394:0.187489:0.447394:0.187489:0.432330:0.153875:0.432330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u + v   x   y +  y –z  = x – z,:@0.186962:0.447499:0.356881:0.447499:0.356881:0.432463:0.186962:0.432463:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
= –:@0.220594:0.447394:0.252326:0.447394:0.252326:0.432330:0.220594:0.432330:0.000000:0.000000:0.000000
(:@0.277462:0.447394:0.282898:0.447394:0.282898:0.432330:0.277462:0.432330:0.000000
):@0.306099:0.447394:0.311534:0.447394:0.311534:0.432330:0.306099:0.432330:0.000000
 :@0.356881:0.447394:0.360663:0.447394:0.360663:0.432330:0.356881:0.432330:0.000000
y la desigualdad:@0.153875:0.463236:0.256529:0.463236:0.256529:0.448172:0.153875:0.448172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| + | ≤ | | + | |  :@0.153875:0.480860:0.263232:0.480860:0.263232:0.465797:0.153875:0.465797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u   v:@0.158009:0.480965:0.189196:0.480965:0.189196:0.465929:0.158009:0.465929:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.212960:0.480965:0.221368:0.480965:0.221368:0.465929:0.212960:0.465929:0.000000
v:@0.245308:0.480965:0.252414:0.480965:0.252414:0.465929:0.245308:0.465929:0.000000
se transforma en:@0.153875:0.498484:0.261755:0.498484:0.261755:0.483421:0.153875:0.483421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| – | ≤ |:@0.153875:0.516108:0.210497:0.516108:0.210497:0.501045:0.153875:0.501045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x   z:@0.158009:0.516214:0.186293:0.516214:0.186293:0.501177:0.158009:0.501177:0.000000:0.000000:0.000000:0.000000:0.000000
x – y:@0.210057:0.516214:0.238870:0.516214:0.238870:0.501177:0.210057:0.501177:0.000000:0.000000:0.000000:0.000000:0.000000
| + |:@0.238430:0.516108:0.263250:0.516108:0.263250:0.501045:0.238430:0.501045:0.000000:0.000000:0.000000:0.000000:0.000000
y –z:@0.262810:0.516214:0.287329:0.516214:0.287329:0.501177:0.262810:0.501177:0.000000:0.000000:0.000000:0.000000
|; :@0.286891:0.516108:0.297322:0.516108:0.297322:0.501045:0.286891:0.501045:0.000000:0.000000:0.000000
esto, en términos de la distancia :@0.153875:0.533732:0.364408:0.533732:0.364408:0.518669:0.153875:0.518669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre dos números reales, se :@0.153875:0.549574:0.339640:0.549574:0.339640:0.534511:0.153875:0.534511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresa como:@0.153875:0.565416:0.244815:0.565416:0.244815:0.550353:0.153875:0.550353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  x, z:@0.153875:0.583146:0.190849:0.583146:0.190849:0.568110:0.153875:0.568110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.166030:0.583041:0.171465:0.583041:0.171465:0.567978:0.166030:0.567978:0.000000
) ≤  (:@0.190849:0.583041:0.230251:0.583041:0.230251:0.567978:0.190849:0.567978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  x, y:@0.212661:0.583146:0.250585:0.583146:0.250585:0.568110:0.212661:0.568110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
) +  (:@0.250585:0.583041:0.291042:0.583041:0.291042:0.567978:0.250585:0.567978:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  y, z:@0.273452:0.583146:0.310373:0.583146:0.310373:0.568110:0.273452:0.568110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
).:@0.310373:0.583041:0.318324:0.583041:0.318324:0.567978:0.310373:0.567978:0.000000:0.000000
que hemos obtenido en la :@0.153875:0.600665:0.328278:0.600665:0.328278:0.585602:0.153875:0.585602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
demostración iv.:@0.153875:0.616507:0.260455:0.616507:0.260455:0.601444:0.153875:0.601444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.720545:0.297267:0.720545:0.297267:0.705072:0.199644:0.705072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199644:0.733113:0.311603:0.733113:0.311603:0.717640:0.199644:0.717640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la siguiente :@0.193071:0.757587:0.329536:0.757587:0.329536:0.742524:0.193071:0.742524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
simbología matemática::@0.153335:0.773429:0.308107:0.773429:0.308107:0.758366:0.153335:0.758366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A la distancia entre dos :@0.153335:0.792836:0.307879:0.792836:0.307879:0.777773:0.153335:0.777773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números reales la denomina-:@0.153335:0.808678:0.340895:0.808678:0.340895:0.793615:0.153335:0.793615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mos :@0.153335:0.824520:0.185173:0.824520:0.185173:0.809457:0.153335:0.809457:0.000000:0.000000:0.000000:0.000000
métrica usual :@0.185173:0.824942:0.284447:0.824942:0.284447:0.809470:0.185173:0.809470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en   y se :@0.284447:0.824520:0.348737:0.824520:0.348737:0.809457:0.284447:0.809457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.304254:0.823635:0.316954:0.823635:0.316954:0.811358:0.304254:0.811358:0.000000
representa por:@0.153335:0.840362:0.248409:0.840362:0.248409:0.825299:0.153335:0.825299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d  x, y =  x – y:@0.153335:0.859874:0.247142:0.859874:0.247142:0.844837:0.153335:0.844837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.165489:0.859768:0.170925:0.859768:0.170925:0.844705:0.165489:0.844705:0.000000
)  |:@0.191259:0.859768:0.218770:0.859768:0.218770:0.844705:0.191259:0.844705:0.000000:0.000000:0.000000:0.000000
|,  x, y    .:@0.246703:0.859768:0.319567:0.859767:0.319567:0.844704:0.246703:0.844705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.289717:0.859741:0.301449:0.859741:0.301449:0.843859:0.289717:0.843859:0.000000
R:@0.304352:0.858882:0.317052:0.858882:0.317052:0.846605:0.304352:0.846605:0.000000