Timeline for Proofs of the uncountability of the reals
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2018 at 13:47 | history | edited | Russ Woodroofe | CC BY-SA 4.0 |
added update on compactness, pedagogical remark
|
| Oct 6, 2017 at 12:38 | comment | added | Russ Woodroofe | I agree there's a detail there, but I think it's straightforward. Measure theory makes it immediate, but isn't necessary. For example, if you use open intervals, you could take a finite subcover of [0,2] by compactness. Now you have a finite set of intervals with total length < 1, which cover an interval of length 2. | |
| Oct 6, 2017 at 11:54 | comment | added | Gerald Edgar | When you say "this is nonsense" you need explanation. One explanation is existence of Lebesgue measure. What you show is: a countable set has measure at most $1$. You also need: the real line has measure ${}> 1$. But (so far) you have not proved that. | |
| Oct 6, 2017 at 10:27 | history | answered | Russ Woodroofe | CC BY-SA 3.0 |