Determine if the sets:
(a){x ∈ Q} ∩ {${1 \over \sqrt{n}}$ : n ∈ N}
(b) {x ∈ R : $x^2 −2>0$ }
Have a minimum, a maximum, an infimum, and a supremum.
For a: If n = 1, ${1 \over \sqrt{n}} = 1 $ and it's a maximum, 1 is also a supremum.
There is't minimus, because if n increases the set decreases but never becomes less then 0 because s is positive. So min = no, infimum = 0.
For b: $x^2 > 2$ and $x > + \sqrt{2}$ and $ x < - \sqrt{2}$
There isn't min or max, infimum is $ - \infty $ and supremum is $ + \infty $
Is it correct and full explanation?