I've seen an explanation that every reducible diagram can be express as the multiplication of irreducible diagrams, however, if we simply multiply all irreducible diagrams together, wouldn't we be multiplying some internal lines more than once, given that one internal lines can connect two one-particle irreducible diagram? Am I missing something?
I understand that there are rigorous explanations using functional methods (like this post), however, I am wondering if there's a more straightforward and intuitive way of proving it, without using functional method.
