Arithmetic, Algebra

The operations of addition and multiplication of ordinary numbers are associative, meaning that if \(a\), \(b\), and \(c\) are numbers, then \((a+b)+c=a+(b+c)\) and \((a\times b)\times c=a\times (b\times c)\). This is not true of either subtraction or division. For instance, \((3-2)-1=0\) but \(3-(2-1)=2\).

Abstract Algebra

There are many examples of abstract algebras that are not associative, for example Lie-algebras.