What Does Uniform Convergence Mean With it's application
Uniform Convergence : Uniform Convergence is a part of real analysis which is discussed in detail below. Definition : Let (X,d) be a metric space and f be a function from X to R . Also for each n ∈ ℕ let fₙ : X ---> R . Then , the sequence of functions <fₙ> converges pointwise to the function f , if for each x ∈ X , the sequence of real numbers < fₙ(x) > converges to the real number f(x) . Therefore <fₙ(x) > converges pointwise to f if lim fₙ(x) = f(x) ∀ x ∈ X . n-->∞ For Example : Let < fₙ > be the sequence defined by fₙ : R --> R such that fₙ(x) = x / n ∀ x∈R , n∈N . Show that the sequence conver...