[Math] Determine the least upper and the greatest lower bounds of the following sets

Question

Determine the least upper and the greatest lower bounds of the following sets:

$a)$ A={${\frac{m} {n} : m,n \in N ,m<2n}$}

$b) $B={${n^{1/2} -[n^{1/2}] : n \in N}$}

my attempts : for option a) if m= n=1 then greatest lower bound will be 1 and if m = 2n ,the the least upper bound will be 2

for option b) here greatest lower bound will be 0… that is $n^{1/2} -n^{1/2}$=0 here i don't know the what is least upper bounds

Pliz verified its and tell me the solution

thanks in advance

Answer 1

Consider (a). All elements of $A$ are between $0$ and $2$. Now think about limits.