Problem 136 (difficulty: 2/10)

Determine the minimum, maximum, infimum, supremum of the following sets (if they have any)!

 (1)  \(\displaystyle [1 , 2]\),      (2)  \(\displaystyle (1 , 2)\),      (3)  \(\displaystyle \{\frac1n: n \in \N^+ \}\),      (4)  \(\displaystyle \Q\),      (5)  \(\displaystyle \{\frac1n + {1 \over \sqrt{n}}: n \in \N^+ \}\),
 (6)  \(\displaystyle \{\root {n} \of 2: n \in \N^+ \}\),      (7)  \(\displaystyle \{x: x \in (0, 1) \cap \Q\}\),      (8)  \(\displaystyle \{\frac1n + {1 \over k}: n, k \in \N^+ \}\),
 (9)  \(\displaystyle \{\sqrt{n+1} - \sqrt{n}: n \in \N^+ \}\),      (10)  \(\displaystyle \{n + \frac1n: n \in \N^+\}\)

Give me another random problem!