Results 1 to 7 of 7

Math Help - Is {} same as {{}} set theory problem

  1. #1
    gsc
    gsc is offline
    Newbie
    Joined
    Oct 2007
    Posts
    2

    Is {} same as {{}} set theory problem

    Ok basic stuff if I have a set A={d,0,{},{{}},1} is this a 5 element set or is {} and {{}} the same ....I think it is 5 elements and thus has 32 elements in its power set but not too sure.....some maths brain put me outta my misery please!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,212
    Thanks
    419
    Awards
    1
    Quote Originally Posted by gsc View Post
    Ok basic stuff if I have a set A={d,0,{},{{}},1} is this a 5 element set or is {} and {{}} the same ....I think it is 5 elements and thus has 32 elements in its power set but not too sure.....some maths brain put me outta my misery please!
    Strictly speaking \{ \} = \emptyset, so \{ \{ \} \} = \{ \emptyset \} which is "the set of elements where the only element is the empty set." It is slightly different in concept to the empty set.

    For example if you were working with sets of sets then \{ \emptyset \} would have to be your "null" element, not simply \emptyset.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    From
    Central Coast, NSW
    Posts
    12
    You are correct. The set {{}} contains a set (that it's the empty set is of no consequence), hence it's non-empty, as opposed to {}.

    EDIT: Too slow ..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,911
    Thanks
    774
    Hello, gsc!

    Here's my baby-talk approach to this . . .


    Is {} and {{}} the same ?
    Think of a set as a paper bag.

    Then \{3\} is a bag containing a 3.
    . . and \{p,q\} is a bag containing p and q.

    And \emptyset \:=\:\{\,\} is a bag containg nothing, an empty bag.


    Note that: . \{0\} is not empty; the bag contains a 0.
    . . . . . \{\text{nothing}\} is not empty; the bag contains a word.

    Then: . \{\emptyset\} \:=\:\{\{\:\}\} is not empty; the bag contains another bag.

    Follow Math Help Forum on Facebook and Google+

  5. #5
    gsc
    gsc is offline
    Newbie
    Joined
    Oct 2007
    Posts
    2

    Post Thank you all very much!

    It's all clear now!
    Thanks for your replies much appreciated....gives me faith in human nature!!! (all you maths genius' helping me, a maths mongo!!). Topsquark thanks for the jokes too.

    Set theory is great but I'm not surprised that Cantor ended up in the loony bin....it all does your head in!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Soroban View Post
    Hello, gsc!

    Here's my baby-talk approach to this . . .


    Think of a set as a paper bag.

    Then \{3\} is a bag containing a 3.
    . . and \{p,q\} is a bag containing p and q.

    And \emptyset \:=\:\{\,\} is a bag containg nothing, an empty bag.


    Note that: . \{0\} is not empty; the bag contains a 0.
    . . . . . \{\text{nothing}\} is not empty; the bag contains a word.

    Then: . \{\emptyset\} \:=\:\{\{\:\}\} is not empty; the bag contains another bag.

    i like that analogy for some reason
    Follow Math Help Forum on Facebook and Google+

  7. #7
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by gsc View Post
    Set theory is great but I'm not surprised that Cantor ended up in the loony bin....it all does your head in!
    hehe. you always hear people say things like that..."math makes you crazy!" I don't think so. i think if a mathematician went crazy, he was inclined to being crazy to begin with and would have ended up crazy even if he had not gotten involved in math. maybe the thing is that math does not make you crazy, but it appeals to you if you are somewhat crazy to begin with
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Set theory problem
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 4th 2011, 06:20 PM
  2. a problem about set theory
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: July 10th 2010, 10:29 AM
  3. Set Theory Problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: May 7th 2010, 08:58 PM
  4. Set Theory problem
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 1st 2010, 12:50 PM
  5. Set theory problem
    Posted in the Math Challenge Problems Forum
    Replies: 4
    Last Post: November 9th 2009, 10:22 PM

Search Tags


/mathhelpforum @mathhelpforum