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We all know the usual representation of ordered pairs in set theory by Kuratowski's definition:
This has several desirable properties:
From here, the usual way to define on ordered triple is by
This fails the first condition, though you could fix it up as
It seems to me though that you could do better in terms of depth and number of {} pairs. I haven't found a better combination yet, but I did find that my first guess:
does not work since one gets (a, a, b) = (a, b, b). It seems likely that no expression of depth 2 will work but I haven't proved this. It also seems likely there is an expression of depth 3 which will work, but I haven't found one yet. Anyone able to find a depth 3 or less expression that satisfies conditions 1 and 2? -- RDBury ( talk) 04:05, 14 May 2017 (UTC)
Mathematics desk | ||
---|---|---|
< May 13 | << Apr | May | Jun >> | May 15 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
We all know the usual representation of ordered pairs in set theory by Kuratowski's definition:
This has several desirable properties:
From here, the usual way to define on ordered triple is by
This fails the first condition, though you could fix it up as
It seems to me though that you could do better in terms of depth and number of {} pairs. I haven't found a better combination yet, but I did find that my first guess:
does not work since one gets (a, a, b) = (a, b, b). It seems likely that no expression of depth 2 will work but I haven't proved this. It also seems likely there is an expression of depth 3 which will work, but I haven't found one yet. Anyone able to find a depth 3 or less expression that satisfies conditions 1 and 2? -- RDBury ( talk) 04:05, 14 May 2017 (UTC)