Yog txhaj tshuaj yog tias thiab tsuas yog?

2024 Tus sau: Elizabeth Oswald | [email protected]. Kawg hloov kho: 2024-01-13 00:07

Claim: f yog txhaj yog thiab tsuas yog nws muaj sab laug sab laug . Pov thawj: Peb yuav tsum (⇒) ua pov thawj tias yog f yog txhaj tshuaj ces nws muaj sab laug inverse, thiab (⇐) tias yog f muaj sab laug inverse, ces nws yog txhaj. (⇒) Piv txwv tias f yog txhaj. Peb xav tsim ib txoj haujlwm g: B→A xws li g ∘ f=id_A.

Puas surjective yog thiab tsuas yog txhaj tshuaj?

Tshwj xeeb, yog tias X thiab Y yog qhov kawg uas muaj tib lub ntsiab lus, ces f: X → Y yog surjective if thiab tsuas yog f yog txhaj. Muab ob teev X thiab Y, cov ntawv sau X ≤ ^{Y yog siv los hais tias X yog khoob lossis tias muaj qhov cuam tshuam los ntawm Y mus rau X.}

Koj paub li cas yog qhov ua haujlwm yog Txhaj?

A muaj nuj nqi f yog txhaj yog thiab tsuas yog thaum twg f(x)=f(y), x=y. yog ib qho kev txhaj tshuaj.

Yuav ua li cas tsis txhaj tshuaj?

Lub luag haujlwm tsis tas yuav txhaj tshuaj lossis qhov kev txiav txim siab kom pom cov duab thim rov qab ntawm lub teeb. Piv txwv li, qhov muaj nuj nqi f(n)=1 nrog domain thiab codomain tag nrho cov zauv ntuj Page 8 2. PROPERTIES OF FUNCTIONS 118 yuav muaj cov duab inverse nram qab no: f−1({1})=N thiab f−1({5, 6, 7, 8, 9})=∅.

Yuav ua li cas txhaj tshuaj?

Hauv kev ua lej, ib qho kev txhaj tshuaj (tseem hu ua kev txhaj tshuaj, lossis ib-rau-ib txoj haujlwm) yog ua haujlwm f uas qhia cov ntsiab lus sib txawv rau cov ntsiab lus sib txawv ; uas yog, f(x₁)=f(x₂) implies x₁=x_{2. Hauv lwm lo lus, txhua lub ntsiab lus ntawm lub luag haujlwm lub codomain yog cov duab ntawm feem ntau ntawm nws lub npe.}