# Help with new arrow notation

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

$$\begin{eqnarray} v \rightarrow v' = v-\eta \nabla C. \tag{15}\end{eqnarray}$$
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. $$\Delta_{V} = v - v'$$.