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In Reply to: And now.... posted by MattC on September 11, 2006 at 17:29:27:
A set can either be a member of itself or not. The set of all mathematical objects is a mathematical object so it's a member of itself. The set of all sets with only three members has an infinite number of members so it's not a member of itself.There must be a set of all sets that are members of themselves and therefore a set of all sets that are not members of themselves. Is that set a member of itself?
This is a problem which has no solution. I leads us to Godel's incompleteness theorem (that no mathematical system can be both consistent and complete) which is an even bigger problem.
Mark Kelly
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Follow Ups
- ""The set of all sets that are not members of themselves" - Mark Kelly 17:44:56 09/11/06 (10)
- When is a set not a set?... - tketcham 13:02:40 09/12/06 (2)
- That was part of the response to Russell's paradox. - Mark Kelly 14:54:39 09/12/06 (1)
- So would this be the VTA paradox... - tketcham 23:00:45 09/12/06 (0)
- You know, I think I might have understood that... - MattC 08:21:08 09/12/06 (0)
- pure chaos ;-) [nt] - OMalley 06:56:25 09/12/06 (0)
- Could you please translate that into English? I got lost by the bakery. )MT( - J. S. Bach 05:48:33 09/12/06 (1)
- Join the rest of us Buns! :-) (nt) - Garth 06:29:37 09/12/06 (0)
- I would very much appreciate - Fred J 01:24:09 09/12/06 (0)
- Re: ""The set of all sets that are not members of themselves" - raphsdad 18:17:54 09/11/06 (0)
- I need a drink...no....actually I think you need the drink more..************** - Ernie L 17:54:37 09/11/06 (0)