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## Main Question or Discussion Point

I have the following question:

Let [itex]n\in\mathbb{Z}^{+}[/itex] st. [itex]n[/itex] is not a perfect square. Let [itex]A=\{x\in\mathbb{Q}|x^{2}<n\}[/itex]. Show that [itex]A[/itex] is bounded in [itex]\mathbb{Q}[/itex] but has neither a greatest lower bound or a least upper bound in [itex]\mathbb{Q}[/itex].

To show that [itex]A[/itex] is bounded in [itex]\mathbb{Q}[/itex] I have to show that it has a infimum and a supremum in [itex]\mathbb{Q}[/itex], right? Not sure where to start...

Let [itex]n\in\mathbb{Z}^{+}[/itex] st. [itex]n[/itex] is not a perfect square. Let [itex]A=\{x\in\mathbb{Q}|x^{2}<n\}[/itex]. Show that [itex]A[/itex] is bounded in [itex]\mathbb{Q}[/itex] but has neither a greatest lower bound or a least upper bound in [itex]\mathbb{Q}[/itex].

To show that [itex]A[/itex] is bounded in [itex]\mathbb{Q}[/itex] I have to show that it has a infimum and a supremum in [itex]\mathbb{Q}[/itex], right? Not sure where to start...