Mugone bayinare ndi katundu

A osiyanasiyana mabwenzi kwa anatipatsa chitsanzo limodzi ndi chiwerengero chachikulu mfundo kuyambira matanthauzo awo ndi kusanthula mawunikidwe mokhala chododometsa. A zosiyanasiyana mfundo m'nkhani pa akonzedwa kwamuyaya. Ngakhale pamene akulankhula za mtundu wopangidwa ndi imeneyi inaperekedwa ubale bayinare pakati zosintha angapo. Komanso pakati pa zinthu kapena mawu.

Monga ulamuliro, ndi asapita bayinare ali atalonjeza R, ndiye ngati xRx kwa phindu la × m'munda wa R, chuma amenewa amatchedwa reflexive, kumene × ndi × - wapangidwa zinthu wamaganizo, ndipo R ndi chizindikiro cha mtundu wina wake ubwenzi pakati pa anthu . Pa nthawi yomweyo, ngati maganizo kapena xRy® yRx, akulankhula za chosokonekera boma kumene ® - asadafe chizindikiro, ofanana ndi mgwirizano wa "ngati ... ndiye ..." Ndipo potsiriza, chinawathandiza kumvetsa n'chakuti zolemba (xRy Ùy Rz). ®xRz kumuuza za transitive paubwenzi, ndi chizindikiro cha u - ichi ndi molumikizana.

A ubale bayinare umene uli reflexive, ofananira, ndi transitive akutchedwa pazikhala kufanana ubwenzi. The chiŵerengero cha F - ntchito, ndi a <×, Y> Ine f ndipo <×, z> Ine f akusonyeza kufanana Y = z. Zambiri bayinare ntchito mosavuta ntchito kwa mfundo awiri osavuta anakonza mu dongosolo linalake, ndi kokha mu nkhani iyi, limatipatsa mtengo kwa motsogoleredwa ziŵiri, anatengedwa pa nkhani zosiyanasiyana.

Izo ziyenera kuti f mapu × kuti Y, Ngati f ndi ntchito ya zone tanthauzo m'dera mfundo × ndi Y. Komabe, pamene extrapolates f × pa Y, ndi Y Ine z, ndiye umenewu umatipatsa chakuti mapulogalamu f mu × z. Chitsanzo losavuta: ngati f (x) = 2X imagwira ntchito mwachilungamo umasinthasintha inteja ×, ndiye tinganene kuti f mapu ndi anasaina ya integers onse ambiri adziwe za lonse chomwecho, koma nthawi imeneyi ngakhale manambala. Monga tanena ubale bayinare kuti imodzi reflexive, ofananira, ndi transitive, ndiye ubale pazikhala kufanana.

Zochokera kumwamba, ubale wa pazikhala kufanana anatsimikiza ndi katundu ubale bayinare:

• reflexivity - chiŵerengero (M ~ N);
• chosokonekera - ngati kufanana M ~ N, kudzakhala N ~ M;
• transitivity - ngati awiri kufanana ndi M ~ N N ~ P, chifukwa M ~ P.

Poganizira ntchito katundu ubale bayinare mwatsatanetsatane. Reflexivity - ndi chimodzi mwa zizindikiro za maulalo ena, aliyense mchitidwe waika mayeso ali kufanana ili yokha. Mwachitsanzo, pakati pa manambala ndi = C ndi a³ ndi - kulankhulana reflexive, chifukwa pali nthawizonse = m'ma = m'ma, ndi a³, s³ ndi. Pa nthawi yomweyo, chiŵerengero cha lochitira ndi> m'ma - antireflexive chifukwa cha ndikosatheka wa lochitira ndi> a. The axiom katundu uyu ndiyotengera m'nkhaniyi: aRc® aRa U cRc, apa chizindikiro ® limasonyeza mawu "amatanthauza" (kapena "amatanthauza") ndi U chizindikiro - angoyima "ndi" (kapena molumikizana). Mawu izi ndizoonekeratu kuti ngati chowonadi cha akufunazo woona ndi Arc aRa akuti ndi crc.

Chosokonekera kumatanthauza kuli ubwenzi, komanso ngati zinthu maganizo kubwezedwa, mwachitsanzo ndi symmetrical ubwenzi rearrangement zinthu sichichititsa kusintha kwa mawonekedwe "Khalidwe bayinare." Mwachitsanzo, unansi wa kufanana = m'ma ndi symmetrical chifukwa pazikhala kufanana ubale m'ma = munthu; mofanana a¹s ndi chiweruzo, monga likukwaniritsa s¹a kulankhulana.

Transitive akonzedwa - ndi chuma chimene kukumana lamulo izi: pa ine ×, z Ine Y ® z Ine ×, kumene ® ntchito ngati chizindikiro kuchotsa mawu akuti: "ngati ... ndiye ...". Kulalatira chilinganizo Choncho kuwerenga monga: ". Ngati osadalira pa ×, z uli Y, z monga ntchito ya ×"