Problem 143 (difficulty: 5/10)

What are the suprema and infima of the following sets?

a) \(\displaystyle \{{1\over n}|n\in\N\}\).

b) \(\displaystyle \{{1\over n}|n\in\N\}\cup\{0\}\).

c) \(\displaystyle \{{1\over n}|n\in\N\}\cup\{{-1\over n}|n\in\N\}\).

d) \(\displaystyle \{{1\over n^n}|n\in\N\}\cup \{2,3\}\).

e) \(\displaystyle \{{\cos n\over n^n}|n\in\N\}\cup [-6,-5] \cup (100,101)\).

Give me another random problem!