In the Wikipedia Page for the Fréchet Derivative they say that a function $f:V \to W$ is Fréchet differentiable at $x \in V$ If there exists a linear Operator $A: V \to W$ such that:
$$\lim_{||h|| \to 0} \frac{||f(x+h) -f(x) -A(h)||_W}{||h||_V} = 0$$
My question is: Is $\lim_{||h|| \to 0}$ the same as $\lim_{h \to 0_V}$? Because $||h|| = 0 \iff h = 0_V$.