- #1
Mr Davis 97
- 1,462
- 44
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?