Calc1: Min, Inf, Max and Sup of sets

Question

Simplify the following sets and, if existing, determine Minimum, Maximum, Infimum and Supremum in ℝ and prove your claim.

b) $\bigcup\limits_{z \in \mathbb{Z} } {]z,z + 1[} $

c) $\bigcap\limits_{n \in \mathbb{N} } {[0,\frac{1}{n}]}$ Hint: Use the Archimedean axiom.

---

So my guess would be (edited)

\begin{array}{|c|c|c|} \hline & Min & Inf & Max & Sup \\ \hline b) & - & -∞ & - & +∞ \\ \hline c) & 0 & 0 & 0 & 0 \\ \hline \end{array}

But how do you prove it properly? And are my assumptions correct?

Answer 1

Set B is $\mathbb R-\mathbb Z$, and set C is $\{0\}$. Given that, do you see how to prove it? Both proofs are one sentence.