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Mine above could easily be used to talk about actual financial matters, albeit the way I chose to look at it when I did the math was a tad less than intuitive.
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Following up on what Mike said, all problems in economics and a lot of management are word problems applications of math, like compound interest problems.
Word problems that come out of calculus and such are useful in a lot of engineering situations (movements of fluids through pipes, surface area of solids, etc).
You are not thinking about it in a particularly good way. A negative number is not less than nothing in the sense that it is more nothing, but it is in fact something: only in a the other direction. When you multiply two negatives, you reverse the direction twice, from forwards/positive to backwards/negative and then from backwards/negative, it reverses to forwards/positive.
+1, Mike.
Math is so great.
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