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The vector space of polynomials (possibly of some fixed degree). This is a case where many students, I think, are tempted to privilege the basis $\{ 1, x, x^2, ... \}$, but to do so is to 1) privilege evaluation at $0$ over evaluation at other points, and 2) miss out on the utility of other bases like $\{ 1, x, {x \choose 2}, ... \}$.