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## Main Question or Discussion Point

Hello,

I'm reading Sean Carroll's

I'm reading Sean Carroll's

*Spacetime and Geometry.*When discussing dual vectors, he presents the gradient as the "simplest example of a dual vector" in spacetime. This confuses me because I learned the gradient to be an operator which takes a scalar as input and outputs a vector. The way Carroll presented dual vectors, it seemed that they should do the opposite: take a vector as input and output a scalar. Can someone clear this up for me?