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Problem 7. Let < denote the usual ordering on R. Define a binary relation C on R by x \sqsubseteq y \Longleftrightarrow x^{2}

} x \leq y\right) \text { for all } x, y \in \mathbf{R} \text { (a) Prove that } \sqsubseteq \text { is a linear ordering of } \mathbf{R} \text { . } ^^20(b)^^20Prove^^20that^^20every^^20real^^20number^^20x<0^^20has^^20a^^20\sqsubseteq^^2dsuccessor.^^20

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