Can anyone help me prove a logic statement about limits?
Hi I have this assignment and I am having trouble on going about the proof structure and the process of proving it.
first of all here's the question:
PROVE or DISPROVE the statement:
∀ x ∈ ℝ, ∀ ε ∈ ℝ, ∃ δ ∈ ℝ, ∀ y ∈ ℝ, |x - y|< δ ⇒ |x^2 - y^2| < ε
I'm very confused on how to do this. I know that this is the limit definition as well but I don't know how to go about proving this statement. So can anyone please help me figure this out? Help is much appreciated. Plus can anyone give me some tips on how to tackle statements like this and tips on how to decide whether the statement is to proven or to be disproved. Thank you in advance.