Given, $S\subset \Bbb Q$, where, $S = \{(2n-1)/n:n\in\Bbb N\}$
Find if S has a supremum and infimum in $\Bbb Q$ and $\Bbb R$. If so, what are the values?
My answer:
Supremum in $\Bbb R$ is where the sequence converges as n approaches infintity. Some quick infinite limits shows that it is 2.
Infimum in $\Bbb R$ is when $n=1$, so $(2n-1)/n = (2(1)-1)=1$
I'm a little less certain about $\Bbb Q$. I think it may have the same infimum as $\Bbb R$ and it does not have a supremum but I'm not sure how to show it