Embhalweni onikeziwe kunikezwe izibonelo eziningi zemethrikhi. Khipha isibonelo sesithathu sesilinganiso.
Context:Ngokwezibalo, isikhala semethrikhi siyisethi esihlanganiswe nomqondo wobude phakathi kwezakhi zayo, ngokuvamile ezibizwa ngamaphuzu. Ibanga lilinganiswa ngomsebenzi obizwa ngokuthi i-metric noma i-distance function. Izikhala zemethrikhi ziyisimo esivamile kakhulu sokutadisha imiqondo eminingi yokuhlaziywa kwezibalo kanye nejometri.  Isibonelo esijwayeleke kakhulu sesikhala semethrikhi yisikhala se-Euclidean esinobukhulu obuyi-3 nomqondo waso ojwayelekile wobude. Ezinye izibonelo ezaziwa kakhulu yi-sphere ene-angle distance kanye ne-hyperbolic plane. I-metric ingase ivumelane nomqondo wokufanisa, kunokuba ibe ngokomzimba, ibanga: isibonelo, isethi yezinhlamvu ze-Unicode eziyi-100 ingahlonyiswa ngebanga le-Hamming, elinganisa inani lezinhlamvu ezidinga ukushintshwa ukuze zithole kusuka kolunye ulayini kuya kolunye.  Njengoba zinjengezikhala ezivamile, izikhala zemethrikhi ziyisithuluzi esisetshenziswa emagatsheni amaningi ehlukene ezibalo. Izinhlobo eziningi zezinto zezibalo zinombono wemvelo wobude ngakho-ke zivuma ukwakheka kwesikhala semetric, kufaka phakathi ama-Riemannian manifolds, izikhala ze-vector ezijwayelekile, namagrafu. Ku-algebra engaqondakali, izinombolo ze-p-adic zivela njengezici zokuqedwa kwesakhiwo se-metric ezinombolweni ezinengqondo. Izikhala zemethrikhi nazo zifundwa ngokwazo ku-metric geometry kanye nokuhlaziywa kwezikhala zemethrikhi.  Imibono eminingi eyisisekelo yokuhlaziywa kwezibalo, kufaka phakathi amabhola, ukuphelela, kanye nokufana, i-Lipschitz, nokuqhubeka kwe-Hölder, kungachazwa ekubekeni izikhala zemethrikhi. Eminye imiqondo, njengokuqhubeka, ukuhlangana, kanye namasethi avulekile futhi avaliwe, ingachazwa ngezikhala zemethrikhi, kodwa futhi nasesimweni esijwayelekile sezikhala ze-topological.
I-metric yesithathu noma umsebenzi womkhawulo ohlangane nawo kulesi sibonelo yi-Hamming distance. Ibanga likaHamming lilinganisa inani lezinguquko zezinhlamvu ezidingekayo ukuze kuguqulwe intambo ethile ibe enye.