I'm doing a bit of research for a tech presentation that touches on the subject of [mathematical duality](http://en.wikipedia.org/wiki/Duality_%28mathematics%29). (To be clear, my presentation is not on mathematics or duality, but mentions duality in passing.)


My question for the math folks is, **is it correct to say multiplication is the mathematical dual of division**? Or am I completely misunderstanding mathematical duality?


Wikipedia says,



> 
> the divides and multiple-of relations on the integers
> 
> 
> 


is considered an example of an "order reversing duality". 


So in layman's terms, could a person characterize multiplication/division as an example of mathematical duality?



Is division considered the mathematical dual of multiplication?
You misunderstand duality. A better example is: planes and lines through the origin (in 3-dimensional space). To each plane you can assign the line perpendicular to it, and vice versa. This is more just a pairing of two kinds of objects, it has interesting properties. For example, a collection of lines are contained in one plane if and only if the corresponding perpendicular planes contain one line. Or, the angle between two lines is equal to the angle between the corresponding perpendicular planes. This is where things start to become interesting: certain statements about lines through the origin (in 3-dimensional space) can be reformulated as statements about planes through the origin (in 3-dimensional space). In mathematics this is very useful. It happens, for example, that switching back and forth between the two "worlds" in a duality gradually enhances our understanding in both worlds.


