# Thread: Bounded above and bounded below

1. ## Bounded above and bounded below

Hi,

See Q3 on attatched document. Im preparing for a forthcoming exam and always struggle with these type of questions....

for (i) i got: bounded above = yes; LUB = 1; In set = YES; Bounded Below = YES; GLB = 0; In set = no;

Im more confident on this part but not for the other parts. Any help/guidance?

2. For 3(iv) we have $-\sqrt 11 < x < \sqrt 11$. LUB is $\sqrt 11$ and GLB is $-\sqrt 11$. This is because the rationals are dense in $\Bbb R$. Neither of these numbers are rational because 11 is prime.