Yuav ua li cas thiaj nrhiav tau kev sib raug zoo ntawm kev sib raug zoo?

2024 Tus sau: Fiona Howard | [email protected]. Kawg hloov kho: 2024-01-10 06:38

Hauv txoj hauv kev, kev sib raug zoo R yog qhov sib txawv, tshwj xeeb yog rau txhua tus a thiab b hauv A, yog R (x, y) nrog x ≠ y, ces R (y, x) yuav tsum tsis tuav, lossis, sib npaug, yog R(x, y) thiab R(y, x), ces x=y.

Dab tsi yog qhov kev sib raug zoo ntawm kev sib raug zoo hauv lej?

Cia peb tam sim no nkag siab lub ntsiab lus ntawm kev sib raug zoo antisymmetric. Ib qho kev sib raug zoo R ntawm lub teeb A tau hais tias yog antisymmetric yog tias tsis muaj ib khub ntawm cov ntsiab lus sib txawv ntawm A uas cuam tshuam rau ib leeg los ntawm Rlej, nws yog denoted li: Rau tag nrho a, b ∈ A, Yog (a, b) ∈ R thiab (b, a) ∈ R, ces a=b.

Koj paub li cas yog matrix yog antisymmetric?

A matrix yog symmetric yog thiab tsuas yog tias nws sib npaug rau nws transpose. Tag nrho cov nkag saum toj no lub ntsiab kab pheeb ces kaum ntawm ib tug symmetric matrix yog reflected rau hauv vaj huam sib luag nkag hauv qab kab pheeb ces kaum. Lub matrix yog skew-symmetric yog thiab tsuas yog nws yog qhov ntxeev ntawm nws txoj kev hloov Tag nrho cov kab kab pheeb ces kaum tseem ceeb ntawm lub skew-symmetric matrix yog xoom.

Muaj pes tsawg txoj kev sib raug zoo ntawm A={ A B C tsis muaj qhov sib txawv?

{a, b, c} yog qhov sib txawv, yog tias ob qho tib si "symmetric khub hauv kev sib cuam tshuam, ces nws tsis yog antisymmetric" Ces nws hloov tawm 26−23=56. Cov lus teb yuav tsum yog 27.

Puas muaj kev sib raug zoo sib npaug?

Definition: A binary relation R uas ib R b thiab b R ib txhais tau tias a=b. Saib kuj symmetric, irreflexive, ib feem kev txiav txim. Nco tseg: Tus kev sib txheeb "tsawg dua lossis sib npaug" yog antisymmetric: yog a ≤ b thiab b ≤ a, ces a=b. … Equals (=) yog antisymmetric vim a=b thiab b=a implies a=b.