For real numbers $a, b$, the quantity $ab$ has the property that $$ab = 0 \iff a = 0 \textrm{ or } b = 0$$ On the other hand, the quantity $a^2 + b^2$ has the property that $$a^2 + b^2 = 0 \iff a = 0 \textrm{ and } b = 0$$

Comparing the right-hand side of the two displayed equations above, we see that they are dual to one another (in the sense of the duality principle in Boolean algebra). Is there some way to describe or see this duality in the context of the expressions $ab$ and $a^2 + b^2$ themselves? In what sense are they dual?



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