In the Wikipedia article Taylor series it is said that:
The error incurred in approximating a function by its $n$th-degree Taylor polynomial is called the remainder or residual and is denoted by the function $R_n(x)$.
The article Taylor's theorem clarifies further:
Taylor's theorem describes the asymptotic behavior of the remainder term $$R_k(x) = f(x) - P_k(x),$$ which is the approximation error when approximating $f$ with its Taylor polynomial.
But I would think that the error is of the opposite sign: $P_k(x) - f(x).$ As an analogy, if the true answer is 90 and someone says it is 100 then I think the error incurred is 10, not -10. Which one is correct?