Is division considered the mathematical dual of multiplication? [closed]

I'm doing a bit of research for a tech presentation that touches on the subject of mathematical duality. (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?

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closed as off topic by Todd Trimble♦, Noah Snyder, Mariano Suárez-Alvarez♦, José Figueroa-O'Farrill, Deane YangJan 3 '11 at 20:42

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they are just words and "inverse" is better, more accurate. – Patrick I-Z Jan 3 '11 at 20:31
(1) This is not an appropriate forum for this question. Try math stackexchange instead. (2) I really don't care to be addressed as "math geek", no matter how light-heartedly it's meant. This is a professional forum. If you were consulting a medical doctor online on a professional matter, would you address him or her as "medicine geek"? No? I didn't think so. – Todd Trimble Jan 3 '11 at 20:32
No offense meant. I'm a software geek, so I thought I'd be among similar kin. :-) – Judah Himango Jan 3 '11 at 20:42
I know you didn't mean to offend, but the point is that we don't know one another, and the presumption is a off-putting. No condescension intended, but please remember this is a professional forum. – Todd Trimble Jan 3 '11 at 20:57
For what it's worth, when folks come into the professional forum of StackOverflow, we're addressed as geeks and it's a compliment. I had a mental picture in my head, perhaps planted there by XKCD, that math folks were similar kin, so I thought nothing of it. I now see this community is very much unlike what I had pictured, so I apologize for the apparent insult. – Judah Himango Jan 3 '11 at 21:22