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2011-01-27, 15:05   #320
Mr. P-1

Jun 2003

7·167 Posts

Quote:
 Originally Posted by science_man_88 $\empty$
That's a subset that every set has, It's not a set with an element which is also a subset. It's a set with no elements at all.

2011-01-27, 15:14   #321
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by Mr. P-1 That's a subset that every set has, It's not a set with an element which is also a subset. It's a set with no elements at all.
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 2011-01-27 at 15:16

 2011-01-27, 16:09 #322 CRGreathouse     Aug 2006 135338 Posts The question is to find a set S with 1. $s\in S$, and 2. $s\subseteq S$ 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 2011-01-27 at 16:10 Reason: clarification
2011-01-27, 16:27   #323
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by Mr. P-1 Please give an example of a set with an element which is also a subset. Hint: What subset does every set have?
the only subset every set has has been said to be $\empty$ so he's hinting that $\empty$ is the answer but then claiming it's not.

2011-01-27, 16:46   #324
CRGreathouse

Aug 2006

3×1,993 Posts

Quote:
 Originally Posted by science_man_88 the only subset every set has has been said to be $\empty$ so he's hinting that $\empty$ is the answer but then claiming it's not.

You can freely ignore the hint, if you like. It gives one right answer (which you haven't found yet) but there are others.

2011-01-27, 17:04   #325
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

20C016 Posts

Quote:
 Originally Posted by CRGreathouse You're answering a question he isn't asking. You can freely ignore the hint, if you like. It gives one right answer (which you haven't found yet) but there are others.
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 $\empty$ and the set itself.

2011-01-27, 17:51   #326
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by science_man_88 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 $\empty$ and the set itself.
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?)

2011-01-27, 18:35   #327
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by CRGreathouse 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?)
obviously not as you wouldn't have to ask then.

2011-01-27, 19:39   #328
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by science_man_88 obviously not as you wouldn't have to ask then.
Sure I would have asked. The possibilities are you can (in which case give an example) or you can't (in which case give a reason).

2011-01-27, 20:11   #329
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by CRGreathouse Sure I would have asked. The possibilities are you can (in which case give an example) or you can't (in which case give a reason).
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.

2011-01-27, 22:57   #330
Mr. P-1

Jun 2003

100100100012 Posts

Quote:
 Originally Posted by science_man_88 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 $\empty$ and the set itself.
You're almost there.

If A is a 1-element set, then the only subsets of A are $\empty$ and A itself.

A cannot be an element of A. What could be an element of A?

Last fiddled with by wblipp on 2011-01-28 at 01:48 Reason: fix tags

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