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# distributive

If + and $$\cdot$$ are binary operations on a given set, then we say that $$\cdot$$ is left-distributive over + if for any elements $$a$$, $$b$$, and $$c$$ in the set we have $$a\cdot (b+c)=a\cdot b+a\cdot c$$. Similarly we say that $$\cdot$$ is right-distributive over + if for any elements $$a$$, $$b$$, and $$c$$ in the set we have $$(b+c)\cdot a=b\cdot a+c\cdot a$$. If $$\cdot$$ is both left and right distributive over + then we say simply that it is distributive over +.

The fact that in arithmetic multiplication is distributive over addition is referred to as the distributive property of arithmetic.

Citation Info

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