Timeline for What notions are used but not clearly defined in modern mathematics?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 26, 2021 at 11:25 | history | edited | Vincent | CC BY-SA 4.0 |
obvious tiny grammar fix
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| Jun 21, 2015 at 20:01 | comment | added | user36212 | Effective is a clearly defined concept: there is a Turing Machine which (perhaps for some problem-connected input) will in finite time output the constant (Note: it's quite possible to have an effective upper bound for an uncomputable constant, even a sequence of effective upper bounds provably tending to the constant, which can be confusing). Explicit construction is not well-defined, though - it's always personal taste (You might rule out a brute-force search of log size as it doesn't give you any idea what the resulting object looks like: but this is P-time possible in a construction) | |
| Jun 21, 2015 at 18:22 | comment | added | Zsbán Ambrus | I thought an elementary proof in analytic number theory means a proof that doesn't use complex analysis. However, "elementary" is overloaded so it means different things in different contexts. | |
| Jan 5, 2012 at 22:57 | comment | added | Kaveh | blog post by Bill GASARCH about what is an elementary proof: blog.computationalcomplexity.org/2010/02/… | |
| May 6, 2011 at 6:38 | comment | added | LSpice | How about ‘closed form’ (ams.org/mathscinet/search/publdoc.html?pg1=MR&s1=1699262)? | |
| Feb 28, 2011 at 0:12 | comment | added | Thierry Zell | I always thought that explicit constructions had more to do with decidability than with computational complexity. Many constructions have branchings (if $a \neq 0$, divide by $a$, otherwise do something else...) that are not at all helpful if you cannot decide which branch you should follow. | |
| Feb 26, 2011 at 17:15 | comment | added | darij grinberg | It's good that these are vague, because it guarantees that we can always look for yet more explicit construction, yet more effective bounds and yet more elementary proofs! | |
| Feb 26, 2011 at 16:28 | history | answered | Gil Kalai | CC BY-SA 2.5 |