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Definition of Uniformly Convergence of a Sequence of Function

 A sequence of real function (fn) is said uniformly convergent on a set A⊆ℝ to a limit function f:A→ℝ if and only if for every 𝜺 > 0 there exists N ∈ ℕ such that for every natural number n ≥ N and for every x ∈ A,

|fn(x) - f(x)| < 𝜺

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