The “0” in “f(x) = 0” stands for the zero vector of whichever vector space you map to. If you map to \mathbb{R}^0, then the zero vector is indeed the empty vector because it has no coordinates.
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The “0” in “f(x) = 0” stands for the zero vector of whichever vector space you map to. If you map to \mathbb{R}^0, then the zero vector is indeed the empty vector because it has no coordinates.