# Math Help - Nonempty Subset of Q

1. ## Nonempty Subset of Q

Find a nonempty subset of Q (rational numbers) that is bounded above but has no least upper bound in Q. Justify your claim. Thanks for the help!

2. Originally Posted by jstarks44444
Find a nonempty subset of Q (rational numbers) that is bounded above but has no least upper bound in Q. Justify your claim. Thanks for the help!
What about the set

$\{x| (x \in \mathbb{Q}) \cap (0 \le x^2 < 2) \}$

3. Originally Posted by jstarks44444
Find a nonempty subset of Q (rational numbers) that is bounded above but has no least upper bound in Q. Justify your claim. Thanks for the help!
This is the quintessential example: $\{q\in\mathbb{Q}:q^2<2\}$
Now the details of the proof are yours to do.

4. in general, any set Q ∩ (a,b) (where (a,b) is an open interval of the reals) where b is irrational will do. why is this so?