I am given some subsets of $\mathbb{R}$:
1. $M_a := ]-\infty ,0]$
2. $M_b := [-1 ,0[$
3. $M_c := \mathbb{N}$
4. $M_d := \{\frac1n |n\in\mathbb{N}\}$
5. $M_e := [-1,0] \cup M_d$
I need to check if those subsets are:
- bounded
- closed
- compact
(and to proove my assumptions)
The bounded property seems almost obvious to me, I know it depends on upper and lower bounds (e.g. sup and inf), but does the set need to have both inf and sup to be bounded, or only one of them is sufficient to be called bounded? As for the closed and compact proeprties, I am not very sure what's meant with it.
Thanks in advance.