(a) Let S = (a, b) be an open interval with a, b = R and a < b. Show that [a, b] is the set of all cluster points of S. (b) Let S = Z. Show that S has no cluster points in R. (c) Let S Q. Show that R is the set of all cluster points of S.
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Exercises on cluster points:
![### Exercise on Cluster Points
**(a)** Let \( S = (a, b) \) be an open interval with \( a, b \in \mathbb{R} \) and \( a < b \). Show that \([a, b]\) is the set of all cluster points of \( S \).
**(b)** Let \( S = \mathbb{Z} \). Show that \( S \) has no cluster points in \( \mathbb{R} \).
**(c)** Let \( S = \mathbb{Q} \). Show that \(\mathbb{R}\) is the set of all cluster points of \( S \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97e612ef-1556-436b-b62c-352b280e9e69%2F3c8e31e4-4d67-4e1b-9d5a-72e799982a59%2Fcjykx3_processed.png&w=3840&q=75)
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