Timeline for What practical applications does set theory have?
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7 events
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| Aug 5, 2021 at 21:02 | comment | added | Joel David Hamkins | @Charles I've also been trying for years to find this article, since this point often comes up. I remember reading it in my New York office in some monthly-like journal, but perhaps it wasn't the MAA Monthly. I read it in the mid 1990s, it would have been 1995-97. I'm sorry I can't provide the reference. | |
| Aug 5, 2021 at 16:09 | comment | added | Charles | @JoelDavidHamkins I'd love to see the paper if you ever find it. I couldn't find it with a search at the MAA Monthly site. | |
| May 5, 2010 at 20:33 | comment | added | gowers | I think of this proof as "morally" a pure existence proof, but it happens that it can be made constructive. (I'd say the same about any proof that begins, "Let q_1,q_2,... be an enumeration of the rationals," when it doesn't matter in the slightest what the enumeration is.) I don't have a formalization of this view though. | |
| Jan 2, 2010 at 4:17 | comment | added | Joel David Hamkins | It is interesting to consider whether this argument is a pure existence proof or whether it provides a construction. Many believe the former, and I once even heard Saharon Shelah say this in a conference talk. But actually, the proof is completely constructive! Cantor provides an effective enumeration of the algebraic numbers and an effective means of producing a number not on that list. I once saw an MAA Monthly article detailing the output of a computer program that was written precisely to implement this strategy, and the title was something like, "The number 0.52672... is transcendental". | |
| Jan 2, 2010 at 2:35 | comment | added | Jason Dyer | I believe it is only practical in a negative fashion; knowing that getting certain mechanical constructions exact is a wasted effort. | |
| Jan 1, 2010 at 22:15 | comment | added | Qiaochu Yuan | Yes, but in what sense can the existence of transcendental numbers be said to be "practical" knowledge? | |
| Jan 1, 2010 at 19:42 | history | answered | Noah Snyder | CC BY-SA 2.5 |