What is the mathematical expression for the definition of continuity?

Options :

1. limₓ→𝒸⁡f(x) = f(c) ∀ c ∈ a

2. limₓ→𝒸f(x) = f(c) ∀ c ∈ (a,b)

3. limₓ→𝒸f(x) = f(c) ∀ c ∈ b

4. limₓ→ₐ⁡f(x) = f(c) ∀ c ∈ (a,b)