149:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, métrico, numérico y variacional:@0.444620:0.043661:0.926912:0.043661:0.926912:0.024916:0.444620:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.2 Propiedades de la adición de vectores:@0.073089:0.136836:0.397358:0.136836:0.397358:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se verifican las siguientes propiedades::@0.073089:0.167776:0.354631:0.167776:0.354631:0.151342:0.073089:0.151342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i. :@0.073089:0.198710:0.084023:0.198710:0.084023:0.182276:0.073089:0.182276:0.000000:0.000000:0.000000
 :@0.103290:0.198710:0.107322:0.198710:0.107322:0.182276:0.103290:0.182276:0.000000
Conmutativa::@0.107248:0.198710:0.209469:0.198710:0.209469:0.182040:0.107248:0.182040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 para todo  ,      ,              .:@0.209353:0.198710:0.462935:0.198710:0.462935:0.182276:0.209353:0.182276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.288044:0.198710:0.312084:0.198710:0.312084:0.182304:0.288044:0.182304:0.000000:0.000000:0.000000
[:@0.315968:0.198571:0.331301:0.198571:0.331301:0.184523:0.315968:0.184523:0.000000
V u:@0.335167:0.198710:0.365781:0.198710:0.365781:0.182304:0.335167:0.182304:0.000000:0.000000:0.000000
2:@0.344210:0.201882:0.349447:0.201882:0.349447:0.192301:0.344210:0.192301:0.000000
1 5 1:@0.369665:0.198155:0.446626:0.198155:0.446626:0.184439:0.369665:0.184439:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.388864:0.198710:0.396595:0.198710:0.396595:0.182304:0.388864:0.182304:0.000000
v:@0.419678:0.198710:0.427409:0.198710:0.427409:0.182304:0.419678:0.182304:0.000000
u:@0.450492:0.198710:0.459806:0.198710:0.459806:0.182304:0.450492:0.182304:0.000000
En la Figura 2.4. se muestra el resultado              .:@0.103220:0.229650:0.496289:0.229650:0.496289:0.213216:0.103220:0.213216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.389821:0.229650:0.399135:0.229650:0.399135:0.213244:0.389821:0.213244:0.000000
1 5 1:@0.403019:0.229095:0.479980:0.229095:0.479980:0.215379:0.403019:0.215379:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.422218:0.229650:0.429949:0.229650:0.429949:0.213244:0.422218:0.213244:0.000000
v:@0.453032:0.229650:0.460763:0.229650:0.460763:0.213244:0.453032:0.213244:0.000000
u:@0.483846:0.229650:0.493160:0.229650:0.493160:0.213244:0.483846:0.213244:0.000000
ii.   :@0.073089:0.260583:0.107322:0.260583:0.107322:0.244150:0.073089:0.244150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Asociativa::@0.107248:0.260583:0.188264:0.260583:0.188264:0.243914:0.107248:0.243914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 para todo  ,  ,   :@0.188148:0.260583:0.314551:0.260583:0.314551:0.244150:0.188148:0.244150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v w:@0.266839:0.260583:0.310593:0.260583:0.310593:0.244177:0.266839:0.244177:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.314477:0.260445:0.329810:0.260445:0.329810:0.246396:0.314477:0.246396:0.000000
V u:@0.329718:0.260583:0.360356:0.260583:0.360356:0.244177:0.329718:0.244177:0.000000:0.000000:0.000000
2:@0.338783:0.263756:0.344020:0.263756:0.344020:0.254175:0.338783:0.254175:0.000000
,    (     )   (     )    .:@0.343974:0.260583:0.546561:0.260583:0.546561:0.244150:0.343974:0.244150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 1:@0.364240:0.260029:0.411234:0.260029:0.411234:0.246313:0.364240:0.246313:0.000000:0.000000:0.000000
v:@0.384286:0.260583:0.392017:0.260583:0.392017:0.244177:0.384286:0.244177:0.000000
w:@0.415099:0.260583:0.427819:0.260583:0.427819:0.244177:0.415099:0.244177:0.000000
5:@0.436489:0.260029:0.451822:0.260029:0.451822:0.246313:0.436489:0.246313:0.000000
u:@0.460473:0.260583:0.469787:0.260583:0.469787:0.244177:0.460473:0.244177:0.000000
1:@0.473671:0.260029:0.489005:0.260029:0.489005:0.246313:0.473671:0.246313:0.000000
v :@0.492870:0.260583:0.503841:0.260583:0.503841:0.244177:0.492870:0.244177:0.000000:0.000000
1:@0.511513:0.260029:0.526847:0.260029:0.526847:0.246313:0.511513:0.246313:0.000000
w:@0.530712:0.260583:0.543431:0.260583:0.543431:0.244177:0.530712:0.244177:0.000000
iii.   :@0.073089:0.291521:0.107322:0.291521:0.107322:0.275087:0.073089:0.275087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Existencia de elemento neutro::@0.106622:0.291521:0.336164:0.291521:0.336164:0.274851:0.106622:0.274851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 existe 0:@0.336087:0.291521:0.392671:0.291521:0.392671:0.275087:0.336087:0.275087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.392468:0.291382:0.407802:0.291382:0.407802:0.277334:0.392468:0.277334:0.000000
V:@0.407599:0.291521:0.416711:0.291521:0.416711:0.275115:0.407599:0.275115:0.000000
2:@0.416552:0.294693:0.421789:0.294693:0.421789:0.285112:0.416552:0.285112:0.000000
, tal que para todo :@0.421683:0.291521:0.553589:0.291521:0.553589:0.275087:0.421683:0.275087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u V u:@0.552853:0.291521:0.606886:0.291521:0.606886:0.275115:0.552853:0.275115:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.562019:0.291382:0.577353:0.291382:0.577353:0.277334:0.562019:0.277334:0.000000
2:@0.586093:0.294693:0.591330:0.294693:0.591330:0.285112:0.586093:0.285112:0.000000
, :@0.591222:0.291521:0.598272:0.291521:0.598272:0.275087:0.591222:0.275087:0.000000:0.000000
1 5 1 5:@0.606739:0.290966:0.694229:0.290966:0.694229:0.277250:0.606739:0.277250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 0:@0.621870:0.291521:0.654782:0.291521:0.654782:0.275087:0.621870:0.275087:0.000000:0.000000:0.000000
u u:@0.669729:0.291521:0.703340:0.291521:0.703340:0.275115:0.669729:0.275115:0.000000:0.000000:0.000000
.:@0.703193:0.291521:0.706396:0.291521:0.706396:0.275087:0.703193:0.275087:0.000000
iv. :@0.073089:0.322458:0.091636:0.322458:0.091636:0.306024:0.073089:0.306024:0.000000:0.000000:0.000000:0.000000
 Existencia de opuestos aditivos::@0.103291:0.322458:0.340783:0.322458:0.340783:0.305789:0.103291:0.305789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 para cada :@0.340487:0.322458:0.416656:0.322458:0.416656:0.306024:0.340487:0.306024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.415938:0.322458:0.425252:0.322458:0.425252:0.306052:0.415938:0.306052:0.000000
[:@0.425086:0.322320:0.440419:0.322320:0.440419:0.308271:0.425086:0.308271:0.000000
V , existe :@0.440199:0.322458:0.505618:0.322458:0.505618:0.306024:0.440199:0.306024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.449374:0.325631:0.454611:0.325631:0.454611:0.316050:0.449374:0.316050:0.000000
v:@0.504895:0.322458:0.512626:0.322458:0.512626:0.306052:0.504895:0.306052:0.000000
[:@0.512460:0.322320:0.527794:0.322320:0.527794:0.308271:0.512460:0.308271:0.000000
V , tal que :@0.527573:0.322458:0.600824:0.322458:0.600824:0.306024:0.527573:0.306024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.536741:0.325631:0.541978:0.325631:0.541978:0.316050:0.536741:0.316050:0.000000
u v u v u:@0.600106:0.322458:0.703297:0.322458:0.703297:0.306052:0.600106:0.306052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 5 1 5:@0.609254:0.321904:0.694204:0.321904:0.694204:0.308188:0.609254:0.308188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.703131:0.322458:0.706334:0.322458:0.706334:0.306024:0.703131:0.306024:0.000000
El elemento  se llama opuesto aditivo de   y se lo nota con :@0.073088:0.353398:0.508695:0.353398:0.508695:0.336964:0.073088:0.336964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v :@0.163596:0.353398:0.174567:0.353398:0.174567:0.336992:0.163596:0.336992:0.000000:0.000000
u:@0.377360:0.353398:0.386674:0.353398:0.386674:0.336992:0.377360:0.336992:0.000000
2:@0.508493:0.352843:0.523826:0.352843:0.523826:0.339128:0.508493:0.339128:0.000000
v:@0.523734:0.353398:0.531465:0.353398:0.531465:0.336992:0.523734:0.336992:0.000000
.:@0.531391:0.353398:0.534594:0.353398:0.534594:0.336964:0.531391:0.336964:0.000000
Considera  , :@0.073051:0.384338:0.165768:0.384338:0.165768:0.367904:0.073051:0.367904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v, w V:@0.149367:0.384338:0.215486:0.384338:0.215486:0.367932:0.149367:0.367932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.191133:0.384199:0.206467:0.384199:0.206467:0.370151:0.191133:0.370151:0.000000
2:@0.215476:0.387504:0.220713:0.387504:0.220713:0.377923:0.215476:0.377923:0.000000
 que se muestra en la Figura 2.5. La suma, :@0.220665:0.384332:0.519601:0.384332:0.519601:0.367898:0.220665:0.367898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v v w:@0.518900:0.384332:0.601806:0.384332:0.601806:0.367926:0.518900:0.367926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.528140:0.383777:0.543473:0.383777:0.543473:0.370061:0.528140:0.370061:0.000000
 y :@0.551039:0.384332:0.566657:0.384332:0.566657:0.367898:0.551039:0.367898:0.000000:0.000000:0.000000
1:@0.573845:0.383777:0.589179:0.383777:0.589179:0.370061:0.573845:0.370061:0.000000
 se muestra en :@0.601732:0.384332:0.710427:0.384332:0.710427:0.367898:0.601732:0.367898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la Figura 2.6. En la Figura 2.7. se muestra :@0.073076:0.400974:0.364542:0.400974:0.364542:0.384540:0.073076:0.384540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.364168:0.400974:0.373482:0.400974:0.373482:0.384568:0.364168:0.384568:0.000000
1 1:@0.373409:0.400419:0.416445:0.400419:0.416445:0.386703:0.373409:0.386703:0.000000:0.000000:0.000000
(:@0.388650:0.400974:0.393528:0.400974:0.393528:0.384540:0.388650:0.384540:0.000000
v:@0.393454:0.400974:0.401185:0.400974:0.401185:0.384568:0.393454:0.384568:0.000000
w) y (:@0.416353:0.400974:0.455192:0.400974:0.455192:0.384540:0.416353:0.384540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.455082:0.400974:0.487294:0.400974:0.487294:0.384568:0.455082:0.384568:0.000000:0.000000:0.000000
1 1:@0.464322:0.400419:0.507358:0.400419:0.507358:0.386703:0.464322:0.386703:0.000000:0.000000:0.000000
):@0.487221:0.400974:0.492099:0.400974:0.492099:0.384540:0.487221:0.384540:0.000000
w:@0.507266:0.400974:0.519986:0.400974:0.519986:0.384568:0.507266:0.384568:0.000000
.:@0.519912:0.400974:0.523115:0.400974:0.523115:0.384540:0.519912:0.384540:0.000000
Se verifica la siguiente propiedad ІІ:@0.073058:0.431914:0.338391:0.431914:0.338391:0.415480:0.073058:0.415480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.338472:0.431914:0.371163:0.431914:0.371163:0.415508:0.338472:0.415508:0.000000:0.000000:0.000000
1:@0.347915:0.431359:0.363248:0.431359:0.363248:0.417643:0.347915:0.417643:0.000000
ІІ   ІІ ІІ :@0.371292:0.431914:0.435285:0.431914:0.435285:0.415480:0.371292:0.415480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
#:@0.384748:0.431359:0.400081:0.431359:0.400081:0.417643:0.384748:0.417643:0.000000
u:@0.413730:0.431914:0.423044:0.431914:0.423044:0.415508:0.413730:0.415508:0.000000
1 :@0.436619:0.431359:0.456738:0.431359:0.456738:0.417643:0.436619:0.417643:0.000000:0.000000
ІІ ІІ, conocida como desigualdad :@0.458266:0.431914:0.710390:0.431914:0.710390:0.415480:0.458266:0.415480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.466356:0.431914:0.474087:0.431914:0.474087:0.415508:0.466356:0.415508:0.000000
triangular.:@0.073039:0.448555:0.145457:0.448555:0.145457:0.432122:0.073039:0.432122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.7.:@0.353179:0.569112:0.426212:0.569112:0.426212:0.552678:0.353179:0.552678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
w:@0.175322:0.512313:0.188041:0.512313:0.188041:0.495906:0.175322:0.495906:0.000000
w:@0.325011:0.512313:0.337730:0.512313:0.337730:0.495906:0.325011:0.495906:0.000000
w:@0.461832:0.505240:0.474552:0.505240:0.474552:0.488834:0.461832:0.488834:0.000000
v:@0.218525:0.479639:0.226256:0.479639:0.226256:0.463233:0.218525:0.463233:0.000000
v:@0.449021:0.533836:0.456752:0.533836:0.456752:0.517430:0.449021:0.517430:0.000000
u    v w:@0.267507:0.476976:0.338909:0.476976:0.338909:0.460570:0.267507:0.460570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 1:@0.280005:0.476422:0.326281:0.476422:0.326281:0.462706:0.280005:0.462706:0.000000:0.000000:0.000000
(:@0.298486:0.476976:0.303364:0.476976:0.303364:0.460543:0.298486:0.460543:0.000000
):@0.338835:0.476976:0.343713:0.476976:0.343713:0.460543:0.338835:0.460543:0.000000
u v:@0.517330:0.492384:0.549543:0.492384:0.549543:0.475978:0.517330:0.475978:0.000000:0.000000:0.000000
1:@0.526570:0.491829:0.541904:0.491829:0.541904:0.478114:0.526570:0.478114:0.000000
(:@0.481270:0.534557:0.486148:0.534557:0.486148:0.518123:0.481270:0.518123:0.000000
v w:@0.486074:0.534557:0.521693:0.534557:0.521693:0.518151:0.486074:0.518151:0.000000:0.000000:0.000000
1 1:@0.493732:0.534002:0.541756:0.534002:0.541756:0.520287:0.493732:0.520287:0.000000:0.000000:0.000000
):@0.521619:0.534557:0.526497:0.534557:0.526497:0.518123:0.521619:0.518123:0.000000
w:@0.541664:0.534557:0.554384:0.534557:0.554384:0.518151:0.541664:0.518151:0.000000
v w:@0.269973:0.518997:0.305591:0.518997:0.305591:0.502591:0.269973:0.502591:0.000000:0.000000:0.000000
1:@0.277631:0.518442:0.292964:0.518442:0.292964:0.504727:0.277631:0.504727:0.000000
u:@0.213850:0.508055:0.223164:0.508055:0.223164:0.491649:0.213850:0.491649:0.000000
u:@0.579933:0.507043:0.589247:0.507043:0.589247:0.490637:0.579933:0.490637:0.000000
u:@0.436688:0.494534:0.446002:0.494534:0.446002:0.478127:0.436688:0.478127:0.000000
2.3 Resta de vectores:@0.073089:0.601055:0.238263:0.601055:0.238263:0.584108:0.073089:0.584108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.073089:0.631995:0.151059:0.631995:0.151059:0.615326:0.073089:0.615326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  , :@0.073089:0.662935:0.126636:0.662935:0.126636:0.646501:0.073089:0.646501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v V:@0.110751:0.662935:0.157376:0.662935:0.157376:0.646529:0.110751:0.646529:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.133299:0.662796:0.148633:0.662796:0.148633:0.648748:0.133299:0.648748:0.000000
2:@0.157048:0.666095:0.162285:0.666095:0.162285:0.656514:0.157048:0.656514:0.000000
. Se define el vector  ,  que pertenece a  , del siguiente modo: :@0.162082:0.662922:0.602139:0.662922:0.602139:0.646489:0.162082:0.646489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.298857:0.662922:0.321728:0.662922:0.321728:0.646516:0.298857:0.646516:0.000000:0.000000:0.000000
V:@0.439185:0.662922:0.448296:0.662922:0.448296:0.646516:0.439185:0.646516:0.000000
2:@0.447965:0.666095:0.453202:0.666095:0.453202:0.656514:0.447965:0.656514:0.000000
u v u:@0.601399:0.662922:0.657063:0.662922:0.657063:0.646516:0.601399:0.646516:0.000000:0.000000:0.000000:0.000000:0.000000
2 5 1 2:@0.610400:0.662368:0.691576:0.662368:0.691576:0.648652:0.610400:0.648652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.671715:0.662922:0.676593:0.662922:0.676593:0.646489:0.671715:0.646489:0.000000
v:@0.691208:0.662922:0.698939:0.662922:0.698939:0.646516:0.691208:0.646516:0.000000
).:@0.698626:0.662922:0.706357:0.662922:0.706357:0.646489:0.698626:0.646489:0.000000:0.000000
La resta de dos vectores se define en términos de la adición de vectores y del opuesto :@0.073111:0.693862:0.710142:0.693862:0.710142:0.677429:0.073111:0.677429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aditivo. Esto es, :@0.073111:0.710504:0.186139:0.710504:0.186139:0.694070:0.073111:0.694070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.185966:0.710504:0.218179:0.710504:0.218179:0.694098:0.185966:0.694098:0.000000:0.000000:0.000000
2:@0.195206:0.709949:0.210540:0.709949:0.210540:0.696234:0.195206:0.696234:0.000000
 se expresa como la suma de   con el opuesto aditivo :@0.218105:0.710504:0.609373:0.710504:0.609373:0.694070:0.218105:0.694070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.430359:0.710504:0.439673:0.710504:0.439673:0.694098:0.430359:0.694098:0.000000
2:@0.609149:0.709949:0.624482:0.709949:0.624482:0.696234:0.609149:0.696234:0.000000
v:@0.624390:0.710504:0.632121:0.710504:0.632121:0.694098:0.624390:0.694098:0.000000
.:@0.632047:0.710504:0.635250:0.710504:0.635250:0.694070:0.632047:0.694070:0.000000
Debido   la existencia de opuestos aditivos, para cada :@0.073074:0.741444:0.493281:0.741444:0.493281:0.725010:0.073074:0.725010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.134610:0.741444:0.143869:0.741444:0.143869:0.725038:0.134610:0.725038:0.000000
v V:@0.494600:0.741444:0.527163:0.741444:0.527163:0.725038:0.494600:0.725038:0.000000:0.000000:0.000000
[:@0.502497:0.741305:0.517830:0.741305:0.517830:0.727257:0.502497:0.727257:0.000000
2:@0.527335:0.744610:0.532572:0.744610:0.532572:0.735029:0.527335:0.735029:0.000000
, existe :@0.532687:0.741438:0.588978:0.741438:0.588978:0.725004:0.532687:0.725004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.590504:0.740883:0.605837:0.740883:0.605837:0.727167:0.590504:0.727167:0.000000
v V:@0.606058:0.741438:0.638620:0.741438:0.638620:0.725032:0.606058:0.725032:0.000000:0.000000:0.000000
[:@0.613955:0.741299:0.629288:0.741299:0.629288:0.727251:0.613955:0.727251:0.000000
2:@0.638781:0.744610:0.644018:0.744610:0.644018:0.735029:0.638781:0.735029:0.000000
, tal que :@0.644133:0.741438:0.710417:0.741438:0.710417:0.725004:0.644133:0.725004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.706349:0.741438:0.710380:0.741438:0.710380:0.725004:0.706349:0.725004:0.000000
v:@0.073103:0.758080:0.080834:0.758080:0.080834:0.741674:0.073103:0.741674:0.000000
1 2 5:@0.080760:0.757525:0.143842:0.757525:0.143842:0.743809:0.080760:0.743809:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.096001:0.758080:0.100879:0.758080:0.100879:0.741646:0.096001:0.741646:0.000000
v:@0.116047:0.758080:0.123778:0.758080:0.123778:0.741674:0.116047:0.741674:0.000000
) 0.:@0.123704:0.758080:0.155862:0.758080:0.155862:0.741646:0.123704:0.741646:0.000000:0.000000:0.000000:0.000000
Sea :@0.073103:0.789020:0.103057:0.789020:0.103057:0.772586:0.073103:0.772586:0.000000:0.000000:0.000000:0.000000
u V:@0.103493:0.789020:0.137252:0.789020:0.137252:0.772614:0.103493:0.772614:0.000000:0.000000:0.000000
[:@0.112807:0.788881:0.128140:0.788881:0.128140:0.774832:0.112807:0.774832:0.000000
2:@0.137260:0.792189:0.142497:0.792189:0.142497:0.782608:0.137260:0.782608:0.000000
. Como   :@0.142500:0.789017:0.213040:0.789017:0.213040:0.772583:0.142500:0.772583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.199695:0.789017:0.209009:0.789017:0.209009:0.772611:0.199695:0.772611:0.000000
2:@0.213478:0.788462:0.228811:0.788462:0.228811:0.774747:0.213478:0.774747:0.000000
v V:@0.228811:0.789017:0.260987:0.789017:0.260987:0.772611:0.228811:0.772611:0.000000:0.000000:0.000000
[:@0.236542:0.788878:0.251876:0.788878:0.251876:0.774830:0.236542:0.774830:0.000000
2:@0.261014:0.792189:0.266251:0.792189:0.266251:0.782608:0.261014:0.782608:0.000000
, se sigue que :@0.266255:0.789017:0.370808:0.789017:0.370808:0.772583:0.266255:0.772583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.371268:0.789017:0.380583:0.789017:0.380583:0.772611:0.371268:0.772611:0.000000
1 2:@0.380583:0.788462:0.416127:0.788462:0.416127:0.774747:0.380583:0.774747:0.000000:0.000000:0.000000
(:@0.395916:0.789017:0.400794:0.789017:0.400794:0.772583:0.395916:0.772583:0.000000
v:@0.416127:0.789017:0.423858:0.789017:0.423858:0.772611:0.416127:0.772611:0.000000
):@0.423858:0.789017:0.428736:0.789017:0.428736:0.772583:0.423858:0.772583:0.000000
[:@0.428736:0.788878:0.444069:0.788878:0.444069:0.774830:0.428736:0.774830:0.000000
V:@0.444069:0.789017:0.453181:0.789017:0.453181:0.772611:0.444069:0.772611:0.000000
2:@0.453228:0.792189:0.458464:0.792189:0.458464:0.782608:0.453228:0.782608:0.000000
. A este elemento se lo ha notado :@0.458469:0.789017:0.710300:0.789017:0.710300:0.772583:0.458469:0.772583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.073094:0.805659:0.105307:0.805659:0.105307:0.789253:0.073094:0.789253:0.000000:0.000000:0.000000
2:@0.082335:0.805104:0.097668:0.805104:0.097668:0.791389:0.082335:0.791389:0.000000
. En la Figura 2.7. se muestran los vectores  ,  , :@0.105233:0.805659:0.440927:0.805659:0.440927:0.789225:0.105233:0.789225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.409800:0.805659:0.433840:0.805659:0.433840:0.789253:0.409800:0.789253:0.000000:0.000000:0.000000
2:@0.440834:0.805104:0.456168:0.805104:0.456168:0.791389:0.440834:0.791389:0.000000
v u:@0.456076:0.805659:0.488969:0.805659:0.488969:0.789253:0.456076:0.789253:0.000000:0.000000:0.000000
 y   :@0.463733:0.805659:0.492927:0.805659:0.492927:0.789225:0.463733:0.789225:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.492853:0.805104:0.508187:0.805104:0.508187:0.791389:0.492853:0.791389:0.000000
v:@0.508095:0.805659:0.515826:0.805659:0.515826:0.789253:0.508095:0.789253:0.000000
.:@0.515752:0.805659:0.518955:0.805659:0.518955:0.789225:0.515752:0.789225:0.000000
Esta operación no cumple con las propiedades conmutativa ni asociativa. Tampoco :@0.073039:0.836599:0.710690:0.836599:0.710690:0.820165:0.073039:0.820165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
posee elemento neutro y no cumple con la existencia de opuestos para la operación :@0.073039:0.853241:0.710072:0.853241:0.710072:0.836807:0.073039:0.836807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resta \ \.:@0.073039:0.869883:0.139084:0.869883:0.139084:0.853449:0.073039:0.853449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.117106:0.869328:0.132439:0.869328:0.132439:0.855612:0.117106:0.855612:0.000000
Figura 2.5:@0.789920:0.470093:0.859823:0.470093:0.859823:0.453659:0.789920:0.453659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.6:@0.789920:0.693768:0.859823:0.693768:0.859823:0.677334:0.789920:0.677334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.8:@0.789920:0.931122:0.859823:0.931122:0.859823:0.914688:0.789920:0.914688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.4:@0.789920:0.339824:0.859823:0.339824:0.859823:0.323390:0.789920:0.323390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.842334:0.421628:0.850065:0.421628:0.850065:0.405222:0.842334:0.405222:0.000000
u:@0.752208:0.430600:0.761522:0.430600:0.761522:0.414194:0.752208:0.414194:0.000000
w:@0.921075:0.418054:0.933794:0.418054:0.933794:0.401648:0.921075:0.401648:0.000000
v:@0.748617:0.256915:0.756348:0.256915:0.756348:0.240509:0.748617:0.240509:0.000000
v:@0.905151:0.257988:0.912882:0.257988:0.912882:0.241581:0.905151:0.241581:0.000000
u:@0.804590:0.316954:0.813904:0.316954:0.813904:0.300548:0.804590:0.300548:0.000000
u:@0.845382:0.201164:0.854696:0.201164:0.854696:0.184758:0.845382:0.184758:0.000000
v u:@0.799371:0.248695:0.831592:0.248695:0.831592:0.232288:0.799371:0.232288:0.000000:0.000000:0.000000
1:@0.807037:0.248140:0.822370:0.248140:0.822370:0.234424:0.807037:0.234424:0.000000
v v:@0.828307:0.269781:0.858944:0.269781:0.858944:0.253374:0.828307:0.253374:0.000000:0.000000:0.000000
1:@0.835971:0.269226:0.851305:0.269226:0.851305:0.255510:0.835971:0.255510:0.000000
u v:@0.833998:0.546032:0.866219:0.546032:0.866219:0.529626:0.833998:0.529626:0.000000:0.000000:0.000000
1:@0.843247:0.545478:0.858580:0.545478:0.858580:0.531762:0.843247:0.531762:0.000000
v:@0.797475:0.587130:0.805206:0.587130:0.805206:0.570724:0.797475:0.570724:0.000000
u:@0.893767:0.561756:0.903081:0.561756:0.903081:0.545350:0.893767:0.545350:0.000000
v w:@0.801910:0.627514:0.837534:0.627514:0.837534:0.611108:0.801910:0.611108:0.000000:0.000000:0.000000
1:@0.809574:0.626960:0.824907:0.626960:0.824907:0.613244:0.809574:0.613244:0.000000
v:@0.834336:0.669327:0.842067:0.669327:0.842067:0.652921:0.834336:0.652921:0.000000
w:@0.757794:0.633232:0.770513:0.633232:0.770513:0.616826:0.757794:0.616826:0.000000
u v:@0.824576:0.896508:0.856795:0.896508:0.856795:0.880102:0.824576:0.880102:0.000000:0.000000:0.000000
2:@0.833823:0.895953:0.849156:0.895953:0.849156:0.882238:0.833823:0.882238:0.000000
u:@0.797949:0.877210:0.807263:0.877210:0.807263:0.860804:0.797949:0.860804:0.000000
v:@0.836371:0.830752:0.844102:0.830752:0.844102:0.814345:0.836371:0.814345:0.000000
u:@0.754308:0.820387:0.763622:0.820387:0.763622:0.803981:0.754308:0.803981:0.000000
2:@0.906573:0.873439:0.921906:0.873439:0.921906:0.859723:0.906573:0.859723:0.000000
v:@0.921814:0.873994:0.929545:0.873994:0.929545:0.857588:0.921814:0.857588:0.000000
2:@0.910163:0.815539:0.925496:0.815539:0.925496:0.801824:0.910163:0.801824:0.000000
v:@0.925404:0.816094:0.933135:0.816094:0.933135:0.799688:0.925404:0.799688:0.000000
DBA 5 (Ev. 1) Localiza objetos geométricos en el plano cartesiano.:@0.075755:0.971366:0.419325:0.971366:0.419325:0.959414:0.075755:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000