Let A ⊂ R. Function f : A → R is continuous in point a ∈ A, if there exists ε > 0, so that with every δ > 0
|f(x) − f(a)| < ε, when x ∈ A and |x − a| < δ.
Is function f : R → R, f(x) = x for all x ∈ R, continuous in point 0 when using this false definition?