Binary noukama vavo zvivako

A-siyana ukama kuti Example rinovira achiperekedzwa vakawanda pfungwa kubva tsanangudzo dzavo uye Analytical Kuongororwa zvokuzviuraya gangaidzo. A siyana pfungwa dzinokurukurwa munyaya panzvimbo nokusingaperi. Kunyange kana kutaura hunyambiri mhando, kubudikidza izvi zvaireva binary ukama pakati variables akawanda. Uyewo pakati zvinhu kana kutaura.

Sezvo kutonga, binary noukama zvinoratidzwa R, ndiko kuti, kana xRx chipi kukosha X mumunda R, imwe pfuma yakadaro inonzi reflexivo, apo X uye X - akaita zvinhu pfungwa, uye R chiratidzo zvimwe zvigadzirwa ukama pakati vanhu . Panguva iyoyowo, kana aiva kana xRy® yRx, rinotaura pamusoro symmetry mamiriro apo ® - airevei chiratidzo, rakafanana Kubatanidzwa "kana ... zvino ..." Uye pakupedzisira, achiongorora zvaive zvakanyorwa (xRy Ùy Rz). ®xRz nezvokukanganisa transitive ukama, pamwe chiratidzo nepfambi - iri pavanoparidza.

A binary ukama kuti zvose reflexivo, symmetric, uye transitive anonzi yokuenzana ukama. Nhamba add - rimwe basa, uye Ini F uye Ini F zvinoreva kuenzana and = z. Simple binary basa rinogona nyore kureva maviri nyore mashoko akarongwa imwe kuti, uye chete muchiitiko ichi, rinotipa ukoshi pauri, akatungamirira izvi zviviri mashoko, akatorwa pane chimwe chiitiko.

Zvinofanira kuti add mepu X kuti ja, Kana f munhu kushanda mapazi tsananguro nzvimbo tsika X uye Y. Zvisinei, kana extrapolates add X pamusoro Y, uye ja Ini z, ipapo ichi zvinotungamirira chokuti add anoratidza zviri X z. A muenzaniso nyore: Kana add (x) = 2x chinoshanda nokuti kumbonyanya zvemasanga integer X, ipapo tichiti add maps of munhu akasaina akagadzirwa integers zvose zvizivikanwe vazhinji chete yose, asi nguva ino kunyange nhamba. Sezvataurwa pamusoro apa, mashoko binary ukama kuti panguva reflexivo, symmetric, uye transitive, ndiye ukama yokuenzana.

Inobva kumusoro, ukama yokuenzana pakutsvaga ehupfumi pamusoro binary ukama:

• reflexivity - nhamba (M ~ N);
• symmetry - kana kuenzana M ~ N, pachava N ~ M;
• transitivity - kana vaviri vakaenzana uye M ~ N N ~ P, mugumisiro M ~ P.

Zvatakurukura kushanda ehupfumi ose binary ukama zvizere. Reflexivity - mumwe zvinoitwa nevamwe Links, apo mumwe chinhu Muedzo seti riri kuenzana ichi pacharo. Somuenzaniso, pakati nhamba imwe = C uye a³ pamwe - reflexivo pakukurukurirana, nekuti pane dzose = C = c, uye a³, s³ pamwe. Panguva iyoyowo, nhamba kusaruramisira ane> C - antireflexive nokuda chisingabviri of kusaruramisira ane> munhu. The axiom pfuma iyi encoded kutaurwa: aRc® Ara U CRC, pano chiratidzo ® inoratidza shoko "zvinoreva" (kana "rinoreva") uye U chiratidzo - inomira ne "uye" (kana tikafunga). Kubva mashoko aya zvinoreva kuti kana chokwadi munhu pfungwa sezvo wechokwadi uye Arc okuti Ara uye CRC.

Symmetry rinobatanidza kuvapo ukama uye kana pfungwa zvinhu kunoshandurwa, kureva zvakafanana, ichibata ukama rearrangement zvinhu haitungamiriri kuchinja chimiro "binary ukama." Somuenzaniso, ukama wakanyatsojeka ane = C iri zvakafanana, ichibata nokuda yokuenzana ukama C = munhu; uyewo kunyatsoenzana a¹s uye kutongwa, sezvo remhosva kukurukurirana s¹a.

Transitive vakaisa - ndiwo pfuma iyo kusangana zvinotevera chinodiwa: pana ini X, z ini ja ® z ini X, apo ® mabasa sechiratidzo kutsiva mashoko: "kana ... zvino ...". Nemashoko fomura saka verenga se: ". Kana pasina X, z ndezvaiye Y, z sezvo kushanda X"