Timeline for Is there a set of criteria to determine whether a number is transcendental for a subset of the reals with positive Lebesgue measure?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2012 at 19:12 | answer | added | Ben Standeven | timeline score: 0 | |
| Jan 24, 2012 at 12:15 | answer | added | Wadim Zudilin | timeline score: 2 | |
| Feb 24, 2011 at 20:16 | answer | added | Gjergji Zaimi | timeline score: 4 | |
| Feb 21, 2011 at 5:09 | comment | added | Stanley Yao Xiao | As a simple example, we can start with Liouville's constant, $\displaystyle \sum_{n=1}^\infty \frac{1}{10^{n!}}$ which can easily proved to be transcendental, and at the same time conclude that $\displaystyle \sum_{n=1}^\infty \frac{a_n}{10^{n!}}$ for any sequence $(a_n)$ such that $a_n = 0,1$ for all $n$ is also transcendental. Thus, we can conclude that an uncountable set of real numbers is transcendental, but this set will have measure 0. | |
| Feb 21, 2011 at 5:09 | comment | added | Sidney Raffer | What does it mean to "test" an arbitrary a set of real numbers of positive measure? Perhaps you would be satisfied with an "explicit" description of a single set of transcendentals of positive measure? If so what counts as "explicit? | |
| Feb 21, 2011 at 3:32 | history | asked | Stanley Yao Xiao | CC BY-SA 2.5 |