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Lyn 8: [[as en slegs as]] ''y'' en ''z'' identies is. Verder as <!-- Moet nog vertaal word▼ :<math>f(y,z) = f(z,y)</math> ▼ vir 'n ''spesifieke'' paar elmente ''y'' en ''z'', dan word gesê dat ''y'' en ''z'', kommuteer. Elke element kommuteer met homself en in 'n [[groep (wiskunde)\|groep]] kommuteer elke element met die [[identiteit (wiskunde)\|identiteit]], met sy eie [[inverse]] en met sy [[eksponent]]. Die bekendste voorbeelde van kommutatiewe binêre bewerkings is [[sommering]] en [[vermenigvuldiging]] van [[reële getal]]le; byvoorbeeld: ~~For example, multiplication of real numbers is commutative since~~ ~~:<math>y z = zy</math>~~ ~~for ''all'' [[real number]]s ''y'' and ''z''. On the other hand, subtraction of real numbers is noncommutative, since~~ ~~:<math>y-z = z-y</math>~~ ~~[[iff]] ''y'' and ''z'' are identical.~~ * 4 + 5 = 5 + 4 (~~since~~aangesien ~~both~~beide [[~~Expression~~Vergelyking (mathematics)\|~~expression~~vergelyking]]s ~~evaluate~~die toresultaat 9 lewer)▼ ~~Additionally, if~~ * 2 × 3 = 3 × 2 (aangesien beidie vergelykings die resultaat van 6 lewer) ▲:<math>f(y,z) = f(z,y)</math> for a ''particular'' pair of elements ''y'' and ''z'', then ''y'' and ''z'' are said to ''commute''. Every element commutes with itself and, in a [[group (mathematics)\|group]], every element commutes with the [[identity (mathematics)\|identity]], with its own [[inverse]], and with its [[exponentiation\|powers]]. ~~The most well-known examples of commutative binary operations are [[addition]] and [[multiplication]] of [[real number]]s; for example:~~ ▲* 4 + 5 = 5 + 4 (since both [[Expression (mathematics)\|expression]]s evaluate to 9) * 2 × 3 = 3 × 2 (since both expressions evaluate to 6) ▲<!-- Moet nog vertaal word Further examples of commutative binary operations include addition and multiplication of [[complex number]]s, addition of [[vector space\|vectors]], and [[intersection (set theory)\|intersection]] and [[union (set theory)\|union]] of [[set]]s. In each case, these operations are commutative over their entire domains.

Kommutatiewe bewerking: Verskil tussen weergawes