Timeline for Terminology for a partition of a set which includes empty sets
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2022 at 8:56 | comment | added | Tom Collinge | @JukkaKohonen Thanks - unordered. | |
| Dec 11, 2022 at 10:37 | comment | added | Jukka Kohonen | Question to the OP: are you looking for ordered or unordered partitions? If not specified, I think partition usually means unordered (= set of sets), not ordered (= sequence of sets). | |
| Dec 11, 2022 at 10:17 | answer | added | Calliope Ryan-Smith | timeline score: 1 | |
| Dec 11, 2022 at 10:11 | answer | added | Martin Brandenburg | timeline score: 2 | |
| Dec 11, 2022 at 10:07 | comment | added | YCor | There is only one empty set (one of the ZF axioms says that two sets with the same elements are equal). Unless you mean partitions as indexed partitions $(A_i)_{i\in I}$, in which case indeed $A_i$ could be equal to the empty set for several $i$. | |
| Dec 11, 2022 at 10:03 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
|
| Dec 11, 2022 at 6:32 | history | edited | Mark Wildon | CC BY-SA 4.0 |
Put maths into LaTeX
|
| Dec 11, 2022 at 6:20 | answer | added | Eric | timeline score: 1 | |
| Oct 24, 2013 at 9:05 | comment | added | Tom Collinge | Actually, if there is more than one empty element of the "partition" I don't think it would invalidate the partition as a set. The set is defined by its extension and so { {}, {}, A, B} = { {}, A, B} is a set - yes ? | |
| Oct 21, 2013 at 7:20 | comment | added | Tom Collinge | Good question. I’m looking at proofs of Cantor-Bernstein theorem. With injections f:A->B and g:B->A, it seems that in creating a bijection A is “divided” into three elements Af which is mapped to B by f; Ag by inverse of g, and Agf which can be mapped by either. Provided the images are disjoint and give B as a union the bijection is proven. However, any one or two of Af, Ag, and Agf could be empty. Can I call this division a “partition” or what else ? | |
| Oct 20, 2013 at 18:41 | comment | added | Will Sawin | Do you mean to allow for more than one empty set? Wouldn't that also be a nonstandard definition of set? | |
| Oct 20, 2013 at 17:03 | history | edited | Andrés E. Caicedo |
edited tags
|
|
| Oct 20, 2013 at 16:11 | vote | accept | Tom Collinge | ||
| Oct 20, 2013 at 12:47 | review | Close votes | |||
| Oct 21, 2013 at 12:11 | |||||
| Oct 20, 2013 at 11:57 | review | First posts | |||
| Oct 20, 2013 at 12:03 | |||||
| Oct 20, 2013 at 11:54 | answer | added | Fred Rohrer | timeline score: 1 | |
| Oct 20, 2013 at 11:38 | history | asked | Tom Collinge | CC BY-SA 3.0 |