Timeline for Real-Closed Fields and Intermediate Value Theorem
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 6, 2021 at 9:02 | comment | added | David Roberts♦ | Part (a) solution: doi.org/10.2307/2318751, and part (b) solution: doi.org/10.2307/2321145 | |
| Jul 5, 2021 at 12:11 | comment | added | Gerald Edgar | @DavidRoberts ... (Rolle's theorm & real-closed) Monthly problem 5861*. Posed 1972, p. 667. Part (a) solved by me, 1975, p. 767. Part (b) solved, 1981, p. 150 . | |
| Jul 5, 2021 at 3:53 | comment | added | David Roberts♦ | @GeraldEdgar do you have a reference? | |
| Mar 17, 2017 at 1:29 | answer | added | Philip Ehrlich | timeline score: 5 | |
| Mar 14, 2017 at 20:12 | history | edited | Philip Ehrlich | CC BY-SA 3.0 |
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| Mar 14, 2017 at 14:37 | comment | added | Philip Ehrlich | @Gerald. On the other hand, the extreme value theorem for polynomials is equivalent to real-closed. (J.M. Gamboa, Journal of Algebra 110 (1987), pp. 1-12.) | |
| Mar 14, 2017 at 14:27 | comment | added | Gerald Edgar | Years ago in the Problems section of the Monthly there was a similar question: In an ordered field, is Rolle's Theorem for polynomials equivalent to real closed? Surprisingly, the answer is "no". | |
| Mar 14, 2017 at 13:28 | history | edited | Philip Ehrlich | CC BY-SA 3.0 |
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| Mar 14, 2017 at 13:22 | comment | added | Philip Ehrlich | Emil, while the right-to-left implication is admittedly not hard to prove (though I wouldn't say trivial), I wonder if the equivalence should be attributed to Artin and Schreier. Neither in their paper nor in van der Waerden's treatment, which was based on Artin's notes, is the equivalence even hinted at. | |
| Mar 14, 2017 at 13:12 | history | edited | Philip Ehrlich | CC BY-SA 3.0 |
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| Mar 14, 2017 at 9:30 | comment | added | Emil Jeřábek | The right-to-left implication is almost trivial, so I'd consider the equivalence to be due to Artin&Schreier... | |
| Mar 14, 2017 at 4:34 | history | edited | Philip Ehrlich | CC BY-SA 3.0 |
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| Mar 13, 2017 at 22:13 | history | asked | Philip Ehrlich | CC BY-SA 3.0 |