Solve the below:
Q1: Explain why this is no good as a definition of continuity at a point a (either by giving an example of a continuous function that does not satisfy the definition or a discontinuous one that does):
Given ε > 0 there exists a δ > 0 such that |x - a| < ε |f(x) - f(a)| < δ
Q2: Can a function be continuous at one value of x and discontinuous at all other x ∈ R? Explain your answer, giving proofs where appropriate