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# 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.

Citation Info

• [MLA] “associative.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 25 Mar 2013. Web. 25 Mar 2013. <http://platonicrealms.com/>
• [APA] associative (25 Mar 2013). Retrieved 25 Mar 2013 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/associative/