Timeline for Irrational number with known probability distribution on digits
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 6, 2017 at 20:45 | comment | added | Aaron Meyerowitz | In brief and informally: the only way known to know that you have a specific distribution on the base $10$ digits of $r$ is to define $r$ via its base $10$ digits (perhaps adding a rational, which can always be defined as an eventually repeating decimal). There is every reason to think that anything else one can describe is normal. The normal reals constitute $99.9999+ \%$ of the reals (all but measure $0$) but no proofs for specific reals to be normal or not are known. | |
| Nov 6, 2017 at 12:14 | answer | added | Kurisuto Asutora | timeline score: 3 | |
| Nov 6, 2017 at 2:08 | answer | added | Igor Rivin | timeline score: 5 | |
| Nov 5, 2017 at 21:36 | comment | added | Gerry Myerson | I expect that for every probability distribution, one can construct an irrational whose digits have that distribution. | |
| Nov 5, 2017 at 17:57 | comment | added | Todd Trimble | To what extent does en.wikipedia.org/wiki/Normal_number#Properties_and_examples not answer your question? The bottom line seems to be that normal numbers (which are by necessity irrational) are known, but none of the classical (computable) irrational numbers like $\pi$ are known to be normal. It is a notorious problem, and it seems to get asked here frequently. Do a search on "normal number" here in MO. | |
| Nov 5, 2017 at 17:21 | history | asked | user3513151 | CC BY-SA 3.0 |