Why does the cut ##(\{x \in \mathbb{Q} | x^2 \le 2 ~ \text{or} ~x < 0 \}, \{x \in \mathbb{Q} | x^2 \ge 2 ~ \text{and} ~x > 0 \})## correspond to ##\sqrt{2}##, and not just ##(\{x \in \mathbb{Q} | x^2 < 2\}, \{x \in \mathbb{Q} | x^2 \ge 2\})##? Why are the additional inequalities involving 0 necessary?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Dedekind cuts

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