Timeline for Superfluous definitions
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 15, 2011 at 15:49 | comment | added | Tom Goodwillie | (of course I meant to write "subsets" when I wrote "members") | |
| Feb 15, 2011 at 14:01 | history | edited | coudy | CC BY-SA 2.5 |
add ref to Bourbaki.
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| Feb 14, 2011 at 5:59 | comment | added | S. Carnahan♦ | I agree with Tom. The empty subset of $X$ is the union of zero subsets of $X$, and zero subsets make a very countable collection. | |
| Feb 14, 2011 at 3:15 | comment | added | Tom Goodwillie | To me it is artificial to require invariance under countable unions without understanding "finite" as a special case of "countable". And the empty set is the union of a finite set of members of any set, namely the empty set of members. | |
| Feb 14, 2011 at 1:44 | comment | added | David Roberts♦ | @Harry, or rather that there are sigma algebras whose set of points is empty. :P | |
| Feb 14, 2011 at 0:49 | comment | added | George Lowther | Also, I think $1\not=0$ in integral domains is similar. | |
| Feb 14, 2011 at 0:48 | comment | added | George Lowther | The empty set axiom of ZF (en.wikipedia.org/wiki/Axiom_of_empty_set) is similar, although in that case it is actually superfluous because the axiom of infinity implies the existence of a set. | |
| Feb 13, 2011 at 21:27 | comment | added | Harry Gindi | Isn't there something strange where the empty set has a pretty good supply of localic sigma-algebras? | |
| Feb 13, 2011 at 21:10 | history | answered | coudy | CC BY-SA 2.5 |