Mabasa Ekubaya, Ekuongorora, uye Ekubatanidza
Mumasvomhu, kunyanya mudzidziso yemashandiro, kune mhando nhatu dzakakosha dzemabasa dzinowanzo kurukurwa: injective, surjective, uye bijective. Imwe neimwe yemhando nhatu idzi dzemabasa ine hunhu hwakasiyana hunosarudza kuti zvinhu kubva patsime (domain) zvinosanganiswa sei nezvinhu zviri muchinangwa (range kana codomain). Chinyorwa chino chichatsanangura tsananguro, hunhu, uye mienzaniso yeimwe neimwe yemabasa aya, pamwe nekushandiswa kwawo muminda yakasiyana-siyana.
Basa rekubaya jekiseni
Basa rekuisa zvinhu panjodzi, rinozivikanwawo sebasa re-one-to-one, ibasa iro chinhu chimwe nechimwe chiri muchikamu chetsime chinosanganiswa nechinhu chakasiyana muchikamu chekuenda. Muchimiro chepamutemo, basa \( f : A \to B \) rinonzi injective kana uye chete kana pa \( a_1, a_2 \in A \), \( f(a_1) = f(a_2) \) zvinoreva kuti \( a_1 = a_2 \).
Zvichinyatsojeka, basa re "injective" rinoita kuti pasave nezvinhu zviviri zvakasiyana mu "source set" zvine mufananidzo wakafanana mu "destination set". Nemamwe mashoko, chinhu chimwe nechimwe mu "destination set" chine chinhu chimwe chete chinoenderana nacho.
Muenzaniso:
– Funga nezvebasa \( f: \mathbb{R} \to \mathbb{R} \) rinotsanangurwa se \( f(x) = 2x + 3 \). Basa iri rinoita sejekiseni nekuti kana \( f(a) = f(b) \), saka \( 2a + 3 = 2b + 3 \), zvinoreva \( a = b \).
Aplikasi:
Mashandiro ekuisa zvinhu munjodzi anowanzo shandiswa mumamiriro ezvinhu atinofanira kuve nechokwadi chekuti hapana kudzokororwa, senge mukunyora kana kunyora makodhi.
Basa reKuvhiya
Basa rekutsvaga, kana kuti basa rekuti on-function, ibasa iro chinhu chimwe nechimwe chiri muchikamu chekuenda \( B \) chine chinhu chimwe chete kubva pachikamu chekubva \( A \) chinoenderana nacho. Mukunyora kwakarongeka, basa \( f : A \kusvika B \) rinonzi surjective kana pa \( b \mu B \), pane chimwe chete \( a \mu A \) zvekuti \( f(a) = b \).
Nemamwe mashoko, basa rekuongorora rinoita kuti nzvimbo yaunoda kuenda ifukidzwe zvakakwana nemufananidzo wenzvimbo yaunoda kuenda. Hapana chinhu chiri munzvimbo yaunoda kuenda chakavharirwa.
Muenzaniso:
– Funga nezvebasa \( f: \mathbb{R} \to \mathbb{R} \) rinotsanangurwa se \( f(x) = x^3 \). Basa iri rinongofungidzira nekuti pa \( y \in \mathbb{R} \), tinogona kuwana \( x \in \mathbb{R} \) zvekuti \( x^3 = y \).
Aplikasi:
Mabasa ekutsvaga anoshandiswa zvakanyanya pakugoverwa kana kugoverwa kwezviwanikwa, kwatinofanira kuva nechokwadi chekuti mugamuchiri wega wega anowana chimwe chinhu kubva kuboka revapi.
Basa reKutarisa Kumativi Ekutanga
Basa rekubijective ibasa rinoita serinopinza uye rinoita serinofungira. Nemamwe mashoko, basa rekubijective rinoita serinoti one-to-one uye onto. Saka, mubasa rekubijective, chinhu chimwe nechimwe chiri muchikamu chesource chinosanganiswa zvakasiyana nechinhu chiri muchikamu chedestination, uye zvakasiyana, chinhu chimwe nechimwe chiri muchikamu chedestination chine chinhu chimwe chete chinochibatanidza kubva muchikamu chesource.
Muenzaniso:
– Funga nezvebasa \( f: \mathbb{R} \to \mathbb{R} \) rinotsanangurwa se \( f(x) = x + 1 \). Basa iri rine bijective nekuti:
– Injecting: Kana \( f(a) = f(b) \), saka \( a + 1 = b + 1 \), zvinoreva \( a = b \).
– Kufungidzira: Pa \( y \mu \mathbb{R} \), tinogona kuwana \( x = y – 1 \) zvekuti \( f(x) = y \).
Aplikasi:
Mabasa eBijective anonyanya kukosha kana tichitarisa shanduko uye isomorphisms, kwatinofanira kuchengetedza chimiro kana hukama huripo pakati pezvinhu patinenge tichigadzira mamapu kubva kune imwe seti kuenda kune imwe. Semuenzaniso, mu cryptography, makiyi e encryption ne decryption anowanzo kuve mabasa e bijective kuitira kuti mameseji agone kuvharwa uye kuvharwa zvakasiyana.
Ongororo Yakawedzerwa
Mifananidzo neMadhayagiramu
Kushandisa dhayagiramu kana girafu yeVenn kunowanzo batsira kunzwisisa mabasa aya. Mudhayagiramu yeVenn, basa rekuisa jekiseni rinogona kuratidzwa nechinhu chimwe nechimwe chiri museti yekuenda chine museve unosvika usingasviki mumwe chete. Basa rekuisa jekiseni rinogona kuratidzwa nechinhu chimwe nechimwe chiri museti yekuenda chine museve unouya unosvika mumwe chete. Basa rekuisa jekiseni rine chinhu chimwe nechimwe museti yekubva nekuenda chine museve unouya mumwe chete, zvichigadzira kubatana kwemunhu mumwe chete.
Basa Rekusiyana
Chimwe chinhu chakakosha chinowanzo dzidzwa mumashoko emabasa ekuisa pfungwa pachinhu chimwe chete, ekufungidzira, uye ekubijective ibasa rekuchinja-chinja.
- Basa rekubaya rinogara riine basa rekuruboshwe rinodzokera kumashure.
- Basa rekufungidzira rinogara riine basa rekuchinja-chinja rakarurama.
- Basa re "bijective" rinogara riine basa rakasiyana re "inverse".
Kana basa riri re "bijective", zvese zviri zviviri "left" ne "right" zvichavapo uye zvese zviri zviviri zvichave zvakaenzana, zvichiumba basa re "true inverse".
Penutup
Kunzwisisa pfungwa dzemabasa ekushandisa zvinhu zvisina kurongwa, zvinoongorora, uye zvinoongorora zvinhu zvisina kurongwa kwakakosha kumapazi mazhinji emasvomhu uye mashandisirwo azvo. Mabasa ekushandisa zvinhu zvisina kurongwa anoita kuti pasave nekudzokororwa; mabasa ekushandisa zvinhu zvisina kurongwa anoita kuti pave nekufukidzwa kwakazara; uye mabasa ekushandisa zvinhu zvisina kurongwa anovimbisa kutaurirana kwemunhu mumwe chete pakati pezvinhu zviviri. Ruzivo rwemhando nhatu dzemabasa aya rwakakosha kwete mumasvomhu chete asiwo muminda yakaita sesainzi yemakombiyuta, economics, uye engineering. Kunzwisisa kwakakwana mashandiro uye mashandisirwo emabasa aya kunogona kuvhura mukana wekuongorora uye kugadzirisa matambudziko zvinobudirira uye zvinobudirira.
