Question

Let \(S = \{x| x^3 <1\} \), find sup S . Is S bounded below.
Please, help

Answer 1

By using a graph, I can see sup S =1 and S is not bounded below, but I don't know how to put it on algebraic way.

Answer 2

its bounded when its have a limit , when the limit is infinite then its not bounded

Answer 3

@ikram002p I love you girl, my best friend. You are always helping me

Answer 4

How?

Answer 5

find the limit when x^3 goes to -infinity

Answer 6

sorry when x goes

Answer 7

oh, so lim S = -infity

Answer 8

and for sup S , find lim when x goes to 1, right?

Answer 9

yes , thus not bounded

Answer 10

sorry i cant even see xD sup means supremum right ?its a value i

Answer 11

yes, it is supremum

Answer 12

ok supremum is a value , now -infinity is a value less than sup ,
find lim S as x-->-infity , which is -infity right ?
thats why its unbounded

Answer 13

Goooooooooot it, hahaha. Thank you so much. The most frustrating is not know how to interpret the stuff in mathematically logic way.

Answer 14

haha its ok :P