for a value to be an upper bound of a set [0,0.5), must it be in the set or can i say that 0.5 is the upper bound of the set?
The best advice I can give a math student is "learn the definitions"! In mathematics (and many other fields) definitions are always "working definitions"- we use the exact words of the definitions proofs or solving problems. I always wonder how students can expect to solve a problem if they don't know the definitions of all the words in the problem!
Now, what is the definition of "upper bound"? (I'll bet it's in your text where they first introduct the term.)
Does it say anything about an "upper bound" for a set being in the set? Does .5 satisfy that definition? For that matter does 500 satisfy that definition?
And be careful to distinguish between "upper bound" and "least upper bound".