# 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!
$\{x| (x \in \mathbb{Q}) \cap (0 \le x^2 < 2) \}$
This is the quintessential example: $\{q\in\mathbb{Q}:q^2<2\}$