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Consider the set ( A = { \frac{1}{n} : n \in \mathbb{N} } \cup { 0, 1, 2 } ). This set is bounded since all its elements are contained within the interval ([0, 2]). The limit points of ( A ) are ( 0 ), ( 1 ), and ( 2 ), as the sequence ( \frac{1}{n} ) approaches ( 0 ) and the constant points ( 1 ) and ( 2 ) are also limit points due to their neighborhoods containing points arbitrarily close to them within the set. Thus, ( A ) has exactly three limit points.

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