This is the Epsilon Delta Definition of Continuity | Real Analysis

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I first came across the neighborhood definition of continuity in Complex Analysis.

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[@vaibhavoutat]

You say the main definition does not require that the limit point c be in the domain of the function, but in the main definition, we have |f(x) - f(c)| < epsilon, how do we plug c here if c is not in the domain of the function.

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Maybe!