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Problem 78: (Infimum And Supremum Of An Interval)
Consider the interval $I=(a,b]$ for some $a,b\in\mathbb{R}$ such that $a<b$. Prove that $I$ is bounded. Then give the minimum, the maximum, the infimum, and the supremum, if possible. Remember to justify each claim you make, by showing the number you have chosen satisfies the corresponding definition, or by showing why the number requested does not exist.
Hint: If you're stuck on this problem because $a$ and $b$ are variables, then replace them with specific numbers and complete the problem. Then go back and change the numbers to $a$ and $b$.
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