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".