I am working through a description of gradient descent and I'm having trouble finding the definition of a couple notations, an arrow and a single quote, v→v′=v−η∇C. I normally express a derivative with a single quote f'(x) but that doesn't appear to be the case here.
The source of this equation is here http://neuralnetworksanddeeplearning.com/chap1.html, about 3/4 of the way down.
Thanks
On
$$\begin{eqnarray} v \rightarrow v' = v-\eta \nabla C. \tag{15}\end{eqnarray}$$
is a function which maps the velocity to the derivative of the velocity:
This gives us a way of following the gradient to a minimum, even when C is a function of many variables, by repeatedly applying the update rule $$\begin{eqnarray} v \rightarrow v' = v-\eta \nabla C. \tag{15}\end{eqnarray}$$ You can think of this update rule as defining the gradient descent algorithm. It gives us a way of repeatedly changing the position vv in order to find a minimum of the function C.
It might be read as $v$ tends to $v'$ (v-prime) which is equal to $v$ minus $\eta$ times $\nabla C$.
v-prime, written as $v'$ in the expression is another variable which has something to do with the perturbation $\Delta_{V}$ defined in the link you gave. $\Delta_{V} = v - v'$.