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SSC Pure Mathematics QUESTION #11176
Question 1
The boundary of a subset $B = \left\{\dfrac{1}{n}: n\in\mathbb{N}\right\}$ of $(\mathbb{R},d)$ is:
  • $B$
  • $\{0\}$
  • $B\cup\{0\}$✔️
  • $\emptyset$
Correct Answer Explanation
The boundary $\partial B = \overline{B}\cap\overline{B^c}$. The closure of $B$ is $\overline{B} = B\cup\{0\}$ (since $0$ is the only limit point of $B$). The interior of $B$ is empty (no open interval is contained in $B$). Therefore $\partial B = \overline{B}\setminus B^0 = B\cup\{0\}$.