Bounded above and bounded below

Apr 2010
30
0
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?
 

Attachments

May 2010
274
67
Los Angeles, California
For 3(iv) we have \(\displaystyle -\sqrt 11 < x < \sqrt 11\). LUB is \(\displaystyle \sqrt 11\) and GLB is \(\displaystyle -\sqrt 11\). This is because the rationals are dense in \(\displaystyle \Bbb R\). Neither of these numbers are rational because 11 is prime.