Hey i've been working on this problem for a few days now, just seeing if anyone else has some insight.
∀x ∈ R, ∀ε ∈ R+, ∃δ ∈ R+, ∀y ∈ R, |x – y| < δ ==> |x^2 – y^2| < ε
prove using epsilon-delta structured proof
ive got to the point where
|x^2 – y^2| < δ|x + y|
but am not completely stuck, I think I have to replace y with a constant somehow? any help would be great! thanks in advance!