Mixed Quantifiers and Epsilon-Delta Implication

On week 4, I learned mixed quantifiers. The order of quantifiers is important.
∀ a ∈ A, ∃ b ∈ B, a+b = 5 and ∃ b ∈ B, ∀ a ∈ A, a+b = 5 are different. But if quantifiers are same, then two implications have same meaning.  Epsilon and delta were also introduced this week. They bound x-axis and y-axis respectively. Although I had learned the concept in MAT137, epsilon-delta implication still confused me a little bit. Anyway, both courses covered it and this really helped me understand it.