In Barrett Oneill's Semi-Riemann Geometry there is a definition of tensor component:
Let $\xi=(x^1,\dots ,x^n)$ be a coordinate system on $\upsilon\subset M$. If $A \in \mathscr I^r_s (M)$ the components of $A$ relative to $\xi$ are the real-valued functions $A _j^i, \dots j^i =A(dx^i_1,\dots > ,dx^i_s, \delta_{j 1},\dots, \delta_{j s})$ $i=1,\dots,r,\ j=1,\dots,s$ on $\upsilon$ where all indices run from $1$ to $n=\dim M$.
By the definition above the $i$th component of $X$ relative to $\xi$ is $X(dx^i)$,which is interpreted as $dx^i(X)=X(x^i)$.
I don't understand the last sentence.
Because one-forms are $(0,1)$ tensors we could interpret them like $V(\theta)=\theta(V)$.
So we can do the same thing here: $X(dx^i)=dx^i(X)$. But how did we write $dx^i(X)=X(x^i)$?
Did I make a mistake?