28:@0.067867:0.963104:0.095634:0.963104:0.095634:0.941283:0.067867:0.941283:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9.º EGB:@0.120102:0.967458:0.170641:0.967458:0.170641:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DUA:@0.070720:0.123711:0.114363:0.123711:0.114363:0.103460:0.070720:0.103460:0.000000:0.000000:0.000000
. Representación:@0.114363:0.123082:0.246653:0.123082:0.246653:0.106182:0.114363:0.106182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El conjunto de los números :@0.286308:0.063945:0.764555:0.063945:0.764555:0.027071:0.286308:0.027071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales :@0.286308:0.094120:0.397959:0.094120:0.397959:0.057246:0.286308:0.057246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.400805:0.092904:0.424996:0.092904:0.424996:0.063710:0.400805:0.063710:0.000000
:@0.094760:0.108604:0.183816:0.108604:0.183816:0.011516:0.094760:0.011516:0.000000:0.000000
Los números reales se utilizan para representar cualquier cantidad que resulta de :@0.287495:0.153866:0.907714:0.153866:0.907714:0.137477:0.287495:0.137477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una medición u operación matemática. Es un conjunto que incluye a los números :@0.287495:0.170462:0.907751:0.170462:0.907751:0.154073:0.287495:0.154073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
racionales e irracionales, es decir que pueden ser positivos, negativos o cero, :@0.287495:0.187059:0.907733:0.187059:0.907733:0.170670:0.287495:0.170670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y pueden expresarse en forma decimal o fraccionaria. :@0.287495:0.203655:0.681637:0.203655:0.681637:0.187266:0.287495:0.187266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A partir de un cuadrado, con la ayuda de una regla y compás, podemos obtener un :@0.287495:0.227374:0.907639:0.227374:0.907639:0.210985:0.287495:0.210985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectángulo áureo y el valor del número de oro, como muestra la figura.:@0.287495:0.243970:0.804035:0.243970:0.804035:0.227582:0.287495:0.227582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Este número contiene una parte racional y otra irracional. Es un número :@0.287495:0.457497:0.816159:0.457497:0.816159:0.441108:0.287495:0.441108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
real:@0.816159:0.457497:0.846161:0.457497:0.846161:0.440596:0.816159:0.440596:0.000000:0.000000:0.000000:0.000000
.:@0.846161:0.457497:0.849367:0.457497:0.849367:0.441108:0.846161:0.441108:0.000000
El conjunto de los números reales, que se simboliza por :@0.296992:0.485883:0.732233:0.485883:0.732233:0.469494:0.296992:0.469494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.738185:0.487962:0.782891:0.487962:0.782891:0.471214:0.738185:0.471214:0.000000:0.000000
=:@0.755249:0.486676:0.765366:0.486676:0.765366:0.469734:0.755249:0.469734:0.000000
∪Ι:@0.785249:0.486676:0.807823:0.486676:0.807823:0.469734:0.785249:0.469734:0.000000:0.000000
 está formado por :@0.754926:0.485883:0.898182:0.485883:0.898182:0.469494:0.754926:0.469494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la unión de los números racionales e irracionales.:@0.296999:0.502479:0.654490:0.502479:0.654490:0.486090:0.296999:0.486090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.674819:0.502517:0.684936:0.502517:0.684936:0.485575:0.674819:0.485575:0.000000
∪:@0.704816:0.502517:0.718968:0.502517:0.718968:0.485575:0.704816:0.485575:0.000000
.:@0.739971:0.502479:0.743177:0.502479:0.743177:0.486090:0.739971:0.486090:0.000000
Relación de orden en los números reales:@0.287499:0.543873:0.606899:0.543873:0.606899:0.526973:0.287499:0.526973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para dos números reales   y  , se tiene que::@0.287499:0.567592:0.604121:0.567592:0.604121:0.551203:0.287499:0.551203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.469064:0.567592:0.503782:0.567592:0.503782:0.551231:0.469064:0.551231:0.000000:0.000000:0.000000
i) :@0.287499:0.591311:0.301577:0.591311:0.301577:0.574411:0.287499:0.574411:0.000000:0.000000:0.000000
a:@0.311234:0.591311:0.320503:0.591311:0.320503:0.574950:0.311234:0.574950:0.000000
 =     si    –   = 0:@0.320503:0.591311:0.443599:0.591311:0.443599:0.574922:0.320503:0.574922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.339557:0.591311:0.348826:0.591311:0.348826:0.574950:0.339557:0.574950:0.000000
a b:@0.379729:0.591311:0.415552:0.591311:0.415552:0.574950:0.379729:0.574950:0.000000:0.000000:0.000000
ii) :@0.287499:0.615030:0.306295:0.615030:0.306295:0.598130:0.287499:0.598130:0.000000:0.000000:0.000000:0.000000
a:@0.311234:0.615030:0.320503:0.615030:0.320503:0.598669:0.311234:0.598669:0.000000
 >     si    –   > 0  :@0.320503:0.615030:0.451671:0.615030:0.451671:0.598641:0.320503:0.598641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.339557:0.615030:0.348826:0.615030:0.348826:0.598669:0.339557:0.598669:0.000000
a b:@0.379729:0.615030:0.415552:0.615030:0.415552:0.598669:0.379729:0.598669:0.000000:0.000000:0.000000
ii) :@0.287499:0.638749:0.306295:0.638749:0.306295:0.621848:0.287499:0.621848:0.000000:0.000000:0.000000:0.000000
a:@0.311234:0.638749:0.320503:0.638749:0.320503:0.622388:0.311234:0.622388:0.000000
 <     si    –   < 0 :@0.320503:0.638749:0.447635:0.638749:0.447635:0.622360:0.320503:0.622360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.339557:0.638749:0.348826:0.638749:0.348826:0.622388:0.339557:0.622388:0.000000
a b:@0.379729:0.638749:0.415552:0.638749:0.415552:0.622388:0.379729:0.622388:0.000000:0.000000:0.000000
Ejemplo::@0.287499:0.669605:0.350982:0.669605:0.350982:0.652967:0.287499:0.652967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.287499:0.693324:0.306221:0.693324:0.306221:0.676423:0.287499:0.676423:0.000000:0.000000:0.000000
Ordena en forma ascendente los siguientes números reales.:@0.311234:0.693324:0.748147:0.693324:0.748147:0.676935:0.311234:0.676935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
     :@0.287499:0.739683:0.307677:0.739683:0.307677:0.723294:0.287499:0.723294:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.311726:0.725630:0.215829:0.725630:0.215829:0.708688:0.311726:0.708688:0.000000
− −:@0.417740:0.725630:0.220576:0.725630:0.220576:0.708688:0.417740:0.708688:0.000000:0.000000:0.000000
1252;; ;,1252;; ; 10,:@0.321789:0.726045:0.348273:0.726045:0.348273:0.709656:0.321789:0.709656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
11111:@0.384554:0.717276:0.416697:0.717276:0.416697:0.700887:0.384554:0.700887:0.000000:0.000000:0.000000:0.000000:0.000000
333 33:@0.383835:0.736888:0.415978:0.736888:0.415978:0.720499:0.383835:0.720499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1010 10; 10;:@0.427803:0.726045:0.438644:0.726045:0.438644:0.709656:0.427803:0.709656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, 1252;; ;:@0.327852:0.726045:0.420243:0.726045:0.420243:0.709656:0.327852:0.709656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
;;:@0.350002:0.726045:0.357958:0.726045:0.357958:0.709656:0.350002:0.709656:0.000000:0.000000
π − −:@0.399886:0.725630:0.227106:0.725630:0.227106:0.708688:0.399886:0.708688:0.000000:0.000000:0.000000:0.000000:0.000000
π − −:@0.404635:0.725630:0.233042:0.725630:0.233042:0.708688:0.404635:0.708688:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.339131:0.726045:0.342338:0.726045:0.342338:0.709656:0.339131:0.709656:0.000000
;52;;:@0.361281:0.726045:0.421948:0.726045:0.421948:0.709656:0.361281:0.709656:0.000000:0.000000:0.000000:0.000000:0.000000
π − −:@0.411165:0.725630:0.238979:0.725630:0.238979:0.708688:0.411165:0.708688:0.000000:0.000000:0.000000:0.000000:0.000000
1212:@0.339004:0.726045:0.364878:0.726045:0.364878:0.709656:0.339004:0.709656:0.000000:0.000000:0.000000:0.000000
52:@0.358832:0.726045:0.393587:0.726045:0.393587:0.709656:0.358832:0.709656:0.000000:0.000000
;:@0.367217:0.726045:0.370423:0.726045:0.370423:0.709656:0.367217:0.709656:0.000000
;;:@0.394692:0.726045:0.416013:0.726045:0.416013:0.709656:0.394692:0.709656:0.000000:0.000000
π −:@0.417100:0.725630:0.344993:0.725630:0.344993:0.708688:0.417100:0.708688:0.000000:0.000000:0.000000
,:@0.351002:0.726045:0.354208:0.726045:0.354208:0.709656:0.351002:0.709656:0.000000
;:@0.373152:0.726045:0.376359:0.726045:0.376359:0.709656:0.373152:0.709656:0.000000
π:@0.423036:0.725630:0.433152:0.725630:0.433152:0.708688:0.423036:0.708688:0.000000
Solución:@0.287495:0.770549:0.351273:0.770549:0.351273:0.753912:0.287495:0.753912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para ordenar los números reales, escribimos cada uno en su notación decimal :@0.287495:0.794268:0.907604:0.794268:0.907604:0.777880:0.287495:0.777880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y los comparamos de acuerdo con las condiciones de orden.:@0.287495:0.810865:0.731485:0.810865:0.731485:0.794476:0.287495:0.794476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
21414:@0.302728:0.853613:0.366267:0.853613:0.366267:0.837224:0.302728:0.837224:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.439167:0.844845:0.448159:0.844845:0.448159:0.828456:0.439167:0.828456:0.000000
3:@0.438429:0.864456:0.447422:0.864456:0.447422:0.848067:0.438429:0.848067:0.000000
0 333:@0.464836:0.853613:0.505690:0.853613:0.505690:0.837224:0.464836:0.837224:0.000000:0.000000:0.000000:0.000000:0.000000
3 141:@0.606213:0.853613:0.645353:0.853613:0.645353:0.837224:0.606213:0.837224:0.000000:0.000000:0.000000:0.000000:0.000000
10:@0.300849:0.881938:0.318742:0.881938:0.318742:0.865549:0.300849:0.865549:0.000000:0.000000
12550 333:@0.345536:0.881938:0.430616:0.881938:0.430616:0.865549:0.345536:0.865549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.316070:0.853198:0.326187:0.853198:0.326187:0.836256:0.316070:0.836256:0.000000
=:@0.451771:0.853198:0.461888:0.853198:0.461888:0.836256:0.451771:0.836256:0.000000
=:@0.593166:0.853198:0.603283:0.853198:0.603283:0.836256:0.593166:0.836256:0.000000
−:@0.290787:0.881523:0.269798:0.881523:0.269798:0.864581:0.290787:0.864581:0.000000
<:@0.321893:0.881523:0.300904:0.881523:0.300904:0.864581:0.321893:0.864581:0.000000
−:@0.335511:0.881523:0.345628:0.881523:0.345628:0.864581:0.335511:0.864581:0.000000
,:@0.334037:0.853613:0.337243:0.853613:0.337243:0.837224:0.334037:0.837224:0.000000
,:@0.474032:0.853613:0.477238:0.853613:0.477238:0.837224:0.474032:0.837224:0.000000
,:@0.614856:0.853613:0.618062:0.853613:0.618062:0.837224:0.614856:0.837224:0.000000
,:@0.351654:0.881938:0.354860:0.881938:0.354860:0.865549:0.351654:0.865549:0.000000
:@0.366451:0.854484:0.246045:0.854484:0.246045:0.837736:0.366451:0.837736:0.000000
:@0.505285:0.854484:0.384879:0.854484:0.384879:0.837736:0.505285:0.837736:0.000000
:@0.642387:0.854484:0.660814:0.854484:0.660814:0.837736:0.642387:0.837736:0.000000
            :@0.386298:0.853613:0.434726:0.853613:0.434726:0.837224:0.386298:0.837224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
             :@0.525113:0.853613:0.577577:0.853613:0.577577:0.837224:0.525113:0.837224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
π:@0.577521:0.853198:0.587638:0.853198:0.587638:0.836256:0.577521:0.836256:0.000000
1414:@0.462607:0.881938:0.500918:0.881938:0.500918:0.865549:0.462607:0.865549:0.000000:0.000000:0.000000:0.000000
3 141:@0.534622:0.881938:0.573780:0.881938:0.573780:0.865549:0.534622:0.865549:0.000000:0.000000:0.000000:0.000000:0.000000
<:@0.376678:0.881523:0.312771:0.881523:0.312771:0.864581:0.376678:0.864581:0.000000
<:@0.450702:0.881523:0.386795:0.881523:0.386795:0.864581:0.450702:0.864581:0.000000
<:@0.521593:0.881523:0.531710:0.881523:0.531710:0.864581:0.521593:0.864581:0.000000
,:@0.398921:0.881938:0.402127:0.881938:0.402127:0.865549:0.398921:0.865549:0.000000
,:@0.468651:0.881938:0.471857:0.881938:0.471857:0.865549:0.468651:0.865549:0.000000
,:@0.543246:0.881938:0.546452:0.881938:0.546452:0.865549:0.543246:0.865549:0.000000
:@0.430174:0.882809:0.377710:0.882809:0.377710:0.866060:0.430174:0.866060:0.000000
:@0.501065:0.882809:0.448602:0.882809:0.448602:0.866060:0.501065:0.866060:0.000000
  :@0.662749:0.886778:0.670820:0.886778:0.670820:0.870389:0.662749:0.870389:0.000000:0.000000
2:@0.500346:0.276962:0.510487:0.276962:0.510487:0.259129:0.500346:0.259129:0.000000
1:@0.463183:0.392862:0.473324:0.392862:0.473324:0.375029:0.463183:0.375029:0.000000
1:@0.535830:0.392862:0.545971:0.392862:0.545971:0.375029:0.535830:0.375029:0.000000
2:@0.402328:0.345682:0.412469:0.345682:0.412469:0.327849:0.402328:0.327849:0.000000
Φ=:@0.689630:0.340104:0.722747:0.340104:0.722747:0.320113:0.689630:0.320113:0.000000:0.000000
+:@0.736816:0.329758:0.748754:0.329758:0.748754:0.309766:0.736816:0.309766:0.000000
1:@0.726571:0.330255:0.737182:0.330255:0.737182:0.310916:0.726571:0.310916:0.000000
5:@0.766603:0.330255:0.777214:0.330255:0.777214:0.310916:0.766603:0.310916:0.000000
+:@0.490635:0.429500:0.502573:0.429500:0.502573:0.409508:0.490635:0.409508:0.000000
1:@0.480371:0.429989:0.490983:0.429989:0.490983:0.410650:0.480371:0.410650:0.000000
5:@0.520403:0.429989:0.531015:0.429989:0.531015:0.410650:0.520403:0.410650:0.000000
2:@0.747939:0.353401:0.758550:0.353401:0.758550:0.334062:0.747939:0.334062:0.000000
5:@0.526135:0.334984:0.536746:0.334984:0.536746:0.315645:0.526135:0.315645:0.000000
Matemática :@0.159185:0.183186:0.248224:0.183186:0.248224:0.167822:0.159185:0.167822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e historia:@0.177797:0.198274:0.244757:0.198274:0.244757:0.182910:0.177797:0.182910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El número de oro, :@0.126619:0.310186:0.248424:0.310186:0.248424:0.295287:0.126619:0.295287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
también llamado :@0.130673:0.325274:0.248425:0.325274:0.248425:0.310375:0.130673:0.310375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proporción áurea, es un :@0.086899:0.340361:0.248425:0.340361:0.248425:0.325462:0.086899:0.325462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número irracional, :@0.123838:0.355449:0.248424:0.355449:0.248424:0.340550:0.123838:0.340550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
representado por la letra :@0.080918:0.370537:0.248425:0.370537:0.248425:0.355638:0.080918:0.355638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
griega φ (phi) cuyo valor :@0.081923:0.385624:0.248424:0.385624:0.248424:0.370725:0.081923:0.370725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es 1,6180339… que :@0.111877:0.400712:0.248425:0.400712:0.248425:0.385813:0.111877:0.385813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
posee muchas :@0.147509:0.415799:0.248425:0.415799:0.248425:0.400900:0.147509:0.400900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades interesantes :@0.076244:0.430887:0.248424:0.430887:0.248424:0.415988:0.076244:0.415988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y que fue descubierto por :@0.072006:0.445975:0.248422:0.445975:0.248422:0.431076:0.072006:0.431076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los antiguos pitagóricos, :@0.082795:0.461062:0.248424:0.461062:0.248424:0.446163:0.082795:0.446163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no como una expresión :@0.086279:0.476150:0.248424:0.476150:0.248424:0.461251:0.086279:0.461251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aritmética, sino como :@0.100904:0.491238:0.248425:0.491238:0.248425:0.476339:0.100904:0.476339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relación o proporción :@0.100904:0.506325:0.248424:0.506325:0.248424:0.491426:0.100904:0.491426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre dos segmentos de :@0.082661:0.521413:0.248424:0.521413:0.248424:0.506514:0.082661:0.506514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una recta, es decir, una :@0.093198:0.536500:0.248424:0.536500:0.248424:0.521601:0.093198:0.521601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
construcción geométrica. :@0.074402:0.551588:0.248424:0.551588:0.248424:0.536689:0.074402:0.536689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Este número aparece en :@0.083063:0.566676:0.248424:0.566676:0.248424:0.551777:0.083063:0.551777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el diseño, en el arte :@0.115948:0.581763:0.248422:0.581763:0.248422:0.566864:0.115948:0.566864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e incluso en la naturaleza.:@0.073983:0.596851:0.244757:0.596851:0.244757:0.581952:0.073983:0.581952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.090129:0.154026:0.247335:0.154026:0.247335:0.137125:0.090129:0.137125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.071775:0.243766:0.071775:0.238658:0.059693:0.238658:0.059693:0.243766:0.000000
Pixabay:@0.071775:0.238658:0.071775:0.215929:0.059864:0.215929:0.059864:0.238658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.141528:0.752648:0.155865:0.752648:0.155865:0.735900:0.141528:0.735900:0.000000
:@0.162635:0.735139:0.175940:0.735139:0.175940:0.718390:0.162635:0.718390:0.000000
:@0.162635:0.755884:0.174926:0.755884:0.174926:0.739136:0.162635:0.739136:0.000000
:@0.162635:0.776630:0.175940:0.776630:0.175940:0.759881:0.162635:0.759881:0.000000
:@0.138724:0.755751:0.152029:0.755751:0.152029:0.739003:0.138724:0.739003:0.000000
:@0.138724:0.776497:0.151015:0.776497:0.151015:0.759748:0.138724:0.759748:0.000000
:@0.138724:0.797242:0.152029:0.797242:0.152029:0.780493:0.138724:0.780493:0.000000
:@0.112452:0.734654:0.125757:0.734654:0.125757:0.717905:0.112452:0.717905:0.000000
:@0.112452:0.755399:0.124744:0.755399:0.124744:0.738651:0.112452:0.738651:0.000000
:@0.112452:0.776144:0.125757:0.776144:0.125757:0.759396:0.112452:0.759396:0.000000
Q:@0.201187:0.767682:0.216827:0.767682:0.216827:0.745412:0.201187:0.745412:0.000000
':@0.216827:0.772919:0.221591:0.772919:0.221591:0.752193:0.216827:0.752193:0.000000
=:@0.140651:0.705550:0.150174:0.705550:0.150174:0.690891:0.140651:0.690891:0.000000
∪:@0.168647:0.705550:0.181969:0.705550:0.181969:0.690891:0.168647:0.690891:0.000000
Q:@0.182619:0.707991:0.196304:0.707991:0.196304:0.688506:0.182619:0.688506:0.000000
':@0.196304:0.712574:0.200473:0.712574:0.200473:0.694438:0.196304:0.694438:0.000000
     Matemática:@0.115799:0.668677:0.223340:0.668677:0.223340:0.651776:0.115799:0.651776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.30. :@0.290067:0.947919:0.333982:0.947919:0.333982:0.937164:0.290067:0.937164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Establecer relaciones de orden en un conjunto de números reales utilizando la recta numérica y la simbología matemática (=, <, ≤, >, ≥).:@0.333603:0.947919:0.901013:0.947919:0.901013:0.937489:0.333603:0.937489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.31. :@0.290067:0.956720:0.335369:0.956720:0.335369:0.945965:0.290067:0.945965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Calcular adiciones y multiplicaciones con números reales y con términos algebraicos aplicando propiedades en R (propiedad dis-:@0.335495:0.956720:0.901001:0.956720:0.901001:0.946290:0.335495:0.946290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tributiva de la suma respecto del producto).:@0.290067:0.965521:0.480134:0.965521:0.480134:0.955091:0.290067:0.955091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000