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$\mathbb{R}^2 \setminus \mathbb{Q} \times \mathbb{Q}$

Posted: Fri Jul 07, 2017 6:35 am
by Riemann
Is the set $\mathcal{S} = \mathbb{R}^2 \setminus \mathbb{Q} \times \mathbb{Q}$ complete? Give a brief explanation.

Re: $\mathbb{R}^2 \setminus \mathbb{Q} \times \mathbb{Q}$

Posted: Wed Dec 05, 2018 10:41 pm
by Ram_1729
No take a sequence $(2+\frac{\sqrt{2}}{n},\sqrt{2})\to (2,\sqrt{2})$

Re: $\mathbb{R}^2 \setminus \mathbb{Q} \times \mathbb{Q}$

Posted: Thu Dec 06, 2018 7:43 pm
by Riemann
Thank you Ram_1729. Exactly! It was an exam's question!