# What is the use of the $\epsilon$ term in this back-propagation equation?

I am currently looking at different documents to understand back-propagation, mainly at this document. Now, at page 3, there is the $$\epsilon$$ symbol involved:

While I understand the main part of the equation, I don't understand the $$\epsilon$$ factor. Searching for the meaning of the $$\epsilon$$ in math, it means (for example) a error value to be minimized, but why should I multiply with the error (it is denoted as E anyways).

Shouldn't the $$\epsilon$$ be the learning rate in this equation? I think that would be what makes sense, because we want to calculate by how much we want to adjust the weight, and since we calculate the gradient, I think the only thing that's missing is the multiplication with the learning rate. The thing is, isn't the learning rate usually denoted with the $$\alpha$$?

The change in nomenclature from what you expected is Lisa Meeden's choice, for unknown reasons. Those with whom she published in the past used $$\epsilon$$ to represent error, the result of a loss function. Why she did not use $$\alpha$$ may be because the letter $$a$$ was used elsewhere in the formula, but, if that was the reasons, that wasn't a great one.