# associative

### 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.