20110127, 15:05  #320 
Jun 2003
7·167 Posts 

20110127, 15:14  #321 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
then your hint lead me to nothing because it fits you hint of a subset that every set has. the only way i see your hint working is if you see the empty set as a collection of empty sets which means the empty set is a element of the collection we call the empty set.
Last fiddled with by science_man_88 on 20110127 at 15:16 
20110127, 16:09  #322 
Aug 2006
13533_{8} Posts 
The question is to find a set S with
1. , and 2. for some s. For example, {2, 3, 5, 7} is a subset (with four elements) of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and 6 is an element of that set. {1, 2, {1, 2, 3, 4}} is a subset (with three elements) of {1, 2, 3, {1, 2, 3, 4}}, while {1, 2, 3, 4} is an element. But none of the subsets in my examples are elements (members), and none of the elements are subsets. Last fiddled with by CRGreathouse on 20110127 at 16:10 Reason: clarification 
20110127, 16:27  #323 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 

20110127, 16:46  #324  
Aug 2006
3×1,993 Posts 
Quote:
You can freely ignore the hint, if you like. It gives one right answer (which you haven't found yet) but there are others. 

20110127, 17:04  #325 
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
I'm obviously not getting it at all from the question all i can think of is every 1 element set and from his hint the only possibilities I've seen are and the set itself.

20110127, 17:51  #326 
Aug 2006
3·1,993 Posts 
The set S itself isn't a member of S  ZF doesn't allow that, so that won't work. The empty set is a subset of S since it's a subset of everything, but is it an element of S? (Can you choose an S that makes that true?)

20110127, 18:35  #327 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
obviously not as you wouldn't have to ask then.

20110127, 19:39  #328 
Aug 2006
3·1,993 Posts 

20110127, 20:11  #329 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
well if a set can have one element an element is a subset of a set one element in length for all sets that I can think of ( maybe one exception). a set is a collection of individual elements, a subset is a set that has at least one of those elements in it, by that logic 1 element from any set can be a subset.

20110127, 22:57  #330  
Jun 2003
10010010001_{2} Posts 
Quote:
If A is a 1element set, then the only subsets of A are and A itself. A cannot be an element of A. What could be an element of A? Last fiddled with by wblipp on 20110128 at 01:48 Reason: fix tags 

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