Let G be a non-empty set, equipped with a binary operation ∘
We say G is a Group if ∘ satisfies;
1) ∀a,b,c∈G, a ∘ (b ∘ c) = (a ∘ b) ∘ c (Associativity)
2) ∃e∈G, ∀a∈G s.t. a ∘ e = e ∘ a = a (Identity Element)
3) ∀g∈G, ∃a∈G s.t. a ∘ g = g ∘ a = e (Inverse Elements)


Let f: ℝ → ℝ
We say the limit of f(x) approaches L if:
∃L∈ℝ, ∀ε>0, ∃𝛿>0, s.t 0 < |x - c| < 𝛿 => |f(x) - L| < ε