Timeline for Direct proof of irrationality?
Current License: CC BY-SA 3.0
10 events
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| May 24, 2017 at 5:45 | history | edited | Michael Hardy | CC BY-SA 3.0 |
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| Jul 16, 2010 at 17:51 | comment | added | Bill Dubuque | See also the following paper - which is discussed in a handful of posts in the sci.math [thread [1]] I mentioned above. Gerry Myerson. Irrationality via well-ordering, Australian Math. Soc. Gazette 35 (2008) 121-125 austms.org.au/Publ/Gazette/2008/May08/Myerson.pdf [1]:groups.google.com/group/sci.math/msg/b547bca171fc24be [1] sci.math, 20 May 2009, Irrationality of sqrt (n^2 - 1) google.com/groups?selm=y8z3ab08eh3.fsf%40nestle.csail.mit.edu | |
| Jul 15, 2010 at 19:11 | comment | added | Bill Dubuque | I thought it worth emphasis for the reader since rediscoverers often think that such proofs are novel - even professional mathematicians - even number theorists! E.g. Estermann rediscovered such an elementary proof in 1975 and often boasted that it was "the first new proof since Pythagoras" and this claim was supported by some other number-theorists, e.g. Niven. | |
| Jul 15, 2010 at 18:08 | comment | added | Dick Palais | Sure, I realized "my" answer (of course it really is NOT original with me) was not exactly what the the OP asked for. However this proof is so completely elementary---even for the final part, you only have to know what a monic polynomial means---that I thought it might appeal to many readers who looked at this question. | |
| Jul 15, 2010 at 16:53 | comment | added | Bill Dubuque | In fact it generalizes quite widely to show that any PID/Dedekind domain is integrally-closed. It's just a specialization of a the 1-line proof by way of principality of the conductor (denominator) ideal which I mentioned above. See the link in my post for much further discussion. | |
| Jul 15, 2010 at 16:40 | comment | added | Rasmus | According to your first sentence I believe that you provide a proof by contraction which is not what the OP has asked for. | |
| Jul 15, 2010 at 16:37 | history | edited | Dick Palais | CC BY-SA 2.5 |
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| Jul 15, 2010 at 16:37 | comment | added | Dick Palais | Ye, Andres, thanks, don't know what the problem was but it's fixed now. | |
| Jul 15, 2010 at 16:33 | comment | added | Andrés E. Caicedo | There seems to be a problem with your code (the first paragraph is cut off.) | |
| Jul 15, 2010 at 16:31 | history | answered | Dick Palais | CC BY-SA 2.5 |