Timeline for Kuratowski's definition of ordered pairs
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 26 at 20:44 | comment | added | Alexander Pruss | Could it be this? In Kuratowski's definition there is a simple description of what the first and second elements of a pair $z$. The first element of $z$ is the unique member of $\bigcap z$. The second element of $z$ is the unique member of $\bigcup z$ if that has only one member and otherwise the unique member of $\bigcup z\backslash \bigcap z$. | |
| S Aug 11, 2017 at 2:31 | history | suggested | jeq | CC BY-SA 3.0 |
Copied image to imgur.com, as it was not being displayed because of the new https rule. Added link to original image source.
|
| Aug 11, 2017 at 2:08 | review | Suggested edits | |||
| S Aug 11, 2017 at 2:31 | |||||
| Jul 23, 2013 at 19:58 | comment | added | smartcaveman | @HansStricker - the diagrams in the png file | |
| Jul 23, 2013 at 12:46 | comment | added | Hans-Peter Stricker | @smartcaveman: What do you mean? Which notation do you mean? | |
| Jul 12, 2013 at 15:15 | comment | added | smartcaveman | @HansStricker - what is the name of the notation you used for the membership graphs? | |
| Apr 25, 2011 at 23:04 | history | edited | Hans-Peter Stricker | CC BY-SA 3.0 |
added 25 characters in body
|
| Apr 24, 2011 at 9:15 | vote | accept | Hans-Peter Stricker | ||
| Apr 24, 2011 at 8:34 | comment | added | Hans-Peter Stricker | Sorry: 0 is {}, and 1 is {0} = {{}}. | |
| Apr 24, 2011 at 6:15 | comment | added | Pietro Majer | An obvious remark: the aim of these definitions is not to capture the essence of "ordered pair", but just to bring this notion into the language of set theory (in the same spirit of von Neumann's definition of ordinal numbers, for instance). So it really doesn't matter which one we choose. | |
| Apr 24, 2011 at 3:12 | answer | added | Joel David Hamkins | timeline score: 24 | |
| Apr 24, 2011 at 2:46 | comment | added | Theo Johnson-Freyd | @unknown (google): I think the idea in option 4 is that the constants 0 and 1 are fixed and chosen ahead of time --- certainly it doesn't matter up to isomorphism what they are, so set them to be some physical objects, if you like. | |
| Apr 24, 2011 at 1:49 | answer | added | user13113 | timeline score: 20 | |
| Apr 24, 2011 at 0:51 | comment | added | user9072 | What is 1 in 4.? | |
| Apr 24, 2011 at 0:09 | answer | added | Andreas Blass | timeline score: 50 | |
| Apr 23, 2011 at 23:30 | comment | added | SNd | My hypothesis would be that in case of non-Kuratowski definitions one would have some more technical dificulties in development of ordinal arithmetic in ZFC. | |
| Apr 23, 2011 at 23:24 | history | asked | Hans-Peter Stricker | CC BY-SA 3.0 |