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4. The Bolzano-Weierstrass theorem does not necessarily hold in an arbi- trary ordered field F. Find counterexamples when: (a) F is the ordered field of

4. The Bolzano-Weierstrass theorem does not necessarily hold in an arbi- trary ordered field F. Find counterexamples when: (a) F is the ordered field of rational numbers Q. (b) (Extra Credit) F is the ordered field of rational functions. (Google the key words for more details.)

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