mersenneforum.org  

Go Back   mersenneforum.org > Math Stuff > Computer Science & Computational Number Theory

Closed Thread
 
Thread Tools
Old 2011-01-27, 15:05   #320
Mr. P-1
 
Mr. P-1's Avatar
 
Jun 2003

7·167 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
\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.
Mr. P-1 is offline  
Old 2011-01-27, 15:14   #321
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts
Default

Quote:
Originally Posted by Mr. P-1 View Post
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
science_man_88 is offline  
Old 2011-01-27, 16:09   #322
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

135338 Posts
Default

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
CRGreathouse is offline  
Old 2011-01-27, 16:27   #323
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts
Default

Quote:
Originally Posted by Mr. P-1 View Post
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.
science_man_88 is offline  
Old 2011-01-27, 16:46   #324
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

3×1,993 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
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'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.
CRGreathouse is offline  
Old 2011-01-27, 17:04   #325
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

20C016 Posts
Default

Quote:
Originally Posted by CRGreathouse View Post
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.
science_man_88 is offline  
Old 2011-01-27, 17:51   #326
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

3·1,993 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
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?)
CRGreathouse is offline  
Old 2011-01-27, 18:35   #327
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts
Default

Quote:
Originally Posted by CRGreathouse View Post
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.
science_man_88 is offline  
Old 2011-01-27, 19:39   #328
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

3·1,993 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
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).
CRGreathouse is offline  
Old 2011-01-27, 20:11   #329
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts
Default

Quote:
Originally Posted by CRGreathouse View Post
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.
science_man_88 is offline  
Old 2011-01-27, 22:57   #330
Mr. P-1
 
Mr. P-1's Avatar
 
Jun 2003

100100100012 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
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
Mr. P-1 is offline  
Closed Thread

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Basic Number Theory 1 & 2 Nick Number Theory Discussion Group 17 2017-12-23 20:10
Observational Number Theory MattcAnderson Miscellaneous Math 8 2016-01-03 19:43
Number Theory Textbook ThomRuley Math 5 2005-08-28 16:04
number theory help math Homework Help 2 2004-05-02 18:09
A problem of number theory hyh1048576 Puzzles 0 2003-09-28 15:35

All times are UTC. The time now is 21:40.


Sun Nov 28 21:40:00 UTC 2021 up 128 days, 16:08, 0 users, load averages: 1.08, 1.41, 1.38

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.