This is the assignment question, and I need to find sup and inf of this set.
$S$ = $\{\frac2n|n\in\{1,2,3,\cdots\}\}$
I think sup$S$ is 2 and inf$S$ is 0. I think it is intuitively obvious that these answers are true, but how can we formally prove that it is true?
I can prove inf$S$ by letting inf$S$ $\gt$ 0, and then showing that it is a contradiction, but how can we prove that sup$S$=2??
Could you help me please?
The sup is easy since it belongs to your set and $\frac{2}{n}$ is decreasing. The inf is a bit more touchy. First prove that $0$ bounds your set below. Then prove that any number greater than $0$ cannot be a lower bound, hence $0$ is the highest lower bound