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Problem 5: (Using The Completeness Axiom)

Consider the solutions to the inequality $x^2<2$. We can write this using set builder notation as $S=\{ x\mid x^2<2\}$.

  1. Is $S$ bounded above? Prove your claim.
  2. What does the completeness axiom say about this set?
  3. Give $\sup S$, or explain why there is no supremum of $S$.

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