Hauv lej, bijection, bijective muaj nuj nqi, ib-rau-ib tsab ntawv, lossis invertible muaj nuj nqi, yog ua haujlwm nruab nrab ntawm cov ntsiab lus ntawm ob pawg, qhov twg txhua lub ntsiab lus ntawm ib pawg yog ua ke nrog raws nraim ib lub caij ntawm lwm lub teeb, thiab txhua lub caij ntawm lwm lub teeb yog ua ke nrog ib lub caij ntawm thawj txheej.
Dab tsi yog bijection muaj nuj nqi nrog piv txwv?
Xwb, f yog bijective yog hais tias nws yog ib tug-rau-ib tsab xov xwm ntawm cov teev, nyob rau hauv lwm yam lus ob leeg txhaj tshuaj thiab surjective. Piv txwv li: Tus function f(x)=x2 los ntawm cov lej zoo tiag tiag rau cov lej tiag tiag yog ob qho tib si txhaj tshuaj thiab qhov tshwm sim. Yog li nws tseem yog bijective.
Koj ua pov thawj li cas yog tias txoj haujlwm yog kev sib tw?
Raws li lub ntsiab lus ntawm bijection, lub luag haujlwm muab yuav tsum yog ob qho tib si txhaj tshuaj thiab qhov tseeb. Yuav kom ua pov thawj, peb yuav tsum ua pov thawj tias f(a)=c thiab f(b)=c ces a=b. Vim qhov no yog tus lej tiag, thiab nws nyob hauv domain, muaj nuj nqi yog surjective.
Puas yog ib qho kev txhaj tshuaj?
Definition. Ib qho kev sib tw yog ib txoj haujlwm uas yog ob qho tib si txhaj tshuaj thiab kev phais. Yog tias muaj nuj nqi f yog bijection, peb kuj hais tias f yog ib-rau-ib thiab mus rau thiab tias f yog bijective function.
Dab tsi yog qhov txawv ntawm kev ua haujlwm thiab kev ua haujlwm bijective?
Ib txoj haujlwm yog bijective yog tias nws yog ob qho tib si txhaj tshuaj thiab. Ib txoj haujlwm bijective kuj hu ua abijection los yog ib-rau-ib tsab ntawv. Ib txoj haujlwm yog bijective yog thiab tsuas yog tias txhua daim duab ua tau yog mapped los ntawm ib qho kev sib cav.
