Whanaunga ā-rua, me o ratou āhuatanga

He whānui o te whanaungatanga mō ngā huinga tauira tahi e te maha nui o ngā ariā mai i ratou whakamāramatanga me te tātaritanga tātari o mutu lēsoni ngā. He momo o ngā ariā kōrero i roto i te tuhinga i runga i te huinga ake. Ahakoa ka korero e pā ana ki te momo rua, i tenei te tikanga o te he hononga ā-rua i waenganui i te maha o taurangi. Na hoki i waenganui i ngā korero ranei.

Ka rite ki te tikanga, kua tohua nga whanaunga ā-rua e R, e ko, ki te hoki tetahi uara o x i te mara o R, huaina xRx ko te taonga taua whakaata, te wahi x me te x - hanga te ngā o whakaaro, a R ko te tohu o etahi ahua o te hononga i waenganui i ngā tāngata takitahi . I te wa ano, ki te te faaite xRy® yRx ranei, korero reira e pā ana ki hangarite kāwanatanga wahi ® - te tohu pānga, rite ki te uniana o "ki te ... ka ..." Na te hopea, deciphering inscriptions (xRy UY RZ). ®xRz korero e pā ana ki hononga transitive, ki te tohu o u - ko te taha tenei.

huaina te pā ana ā-rua e ko e rua whakaata, hangarite, me transitive te he hononga ōrite. Ko te ōwehenga o te f - he mahi, a no Î f me Î f titau te ōritetanga y = z. Ka taea e mahi Simple ā-rua kia ngāwari tono ki te tautohetohe ohie e rua whakaritea i roto i te tetahi raupapa, me anake i roto i tenei take, e whakarato reira he uara ki reira, whakahaua enei kīanga e rua, tangohia i roto i te take ngā.

kia mea te reira e f mahere x ki y, Ki te f Ko te mahi o te rohe rohe whakamāramatanga uara x me te y. Heoi, ka extrapolates f x runga y, me y Í z, ka arata'i tenei ki te meka e whakaaturanga f i x z. He tauira ohie: ki te he tika hoki tika te noho tōpū x f (x) = 2x, ka mea tatou e f mahere te huinga hainatia o tau tōpū katoa mohiotia ki he tokomaha o te taua katoa, engari tenei wa noa tau. Ka rite ki whakahuatia i runga ake, te hononga ā-rua e wā kotahi whakaata, hangarite, me transitive, ko te hononga o te ōritenga.

I runga anō i te runga ake, te hononga o te ōritenga whakaritea e te āhuatanga o whanaunga ā-rua:

• reflexivity - te ōwehenga (M ~ N);
• hangarite - ki te taurite Tane ~ N, i reira ka kia N ~ M;
• transitivity - ki te rua ōritetanga me M ~ N N ~ P, te hua M ~ P.

Ka whakaaro nga āhuatanga tono o whanaunga ā-rua i roto i te taipitopito atu. Reflexivity - Ko tetahi o nga āhuatanga o te tahi mau hononga, te wahi ia huānga o te huinga whakamātautau kei roto i tenei taurite iho. Hei tauira, i waenganui i nga tau i te = c me a³ ki - kōrero whakaata, no te mea i reira te mea tonu he = c = c, me a³, s³ ki. I te wa ano, i te ōwehenga o te kore ōritenga te> c - antireflexive no o te eita o te kore ōritenga te> he. whakawaeheretia te axiom o tenei taonga te pūāhua: aRc® Ara u CRC, konei te tohu ® tohu te kupu "fakahu'unga" (ranei "fakahu'unga") me te tohu U - tu i "me te" (ranei te taha). Mai i tenei tauākī whai reira e te mea te parau mau o te whakaaro rite Ara faaiteraa pono, me te pewa, me te CRC.

Hangarite e faatupu te oraraa o te hononga me te ra ahani ua taui te taonga hinengaro, arā, e kore e he whakatikatika hononga hangarite o ngā arahi ki te hurihanga o te puka "whanaunga ā-rua." Hei tauira, he hangarite te hononga o te taurite te = c tika ana ki te ōritenga pā ana c = he; hoki rite a¹s me whakawa, kia rite tutaki reira te s¹a kōrero.

Transitive huinga - ko te taonga i roto i nei te whakatau i te whakaritenga e whai ake nei i te reira: i Î x, z Î y ® z Î x, te wahi ® mahi rite te tohu whakakapi i te kupu: "Ki te ... ka ...". Waha tātai kupu lau rite: ". Ki te motuhake o te x, z no y, z rite te mahi o te x"