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Heine's theorem, named after the German mathematician Eduard Heine, establishes a link in mathematical analysis between limits of functions and limits of sequences. The theorem states that the existence and value of the limit of a function at a point can be characterized by the limits of all sequences that converge to that point. Conversely, information about sequential limits can be used to determine function limits. As a consequence, many properties of limits of functions may be derived from the corresponding properties of limits of sequences.
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