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Math Help - theoretical groups proof 1,1

  1. #1
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    theoretical groups proof 1,1

    V is a vectoric space.
    W_1,W_2\subseteq V\\
    W_1\nsubseteq W_2\\
    W_2\nsubseteq W_1\\
    prove that W_1 \cup W_2 is not a vectoric subspace of V.

    i dont ave the shread of idea on how to tackle it
    i only know to prove that some stuff is subspace
    but constant mutiplication
    and by sum of two coppies

    this question here differs a lot
    Last edited by transgalactic; October 26th 2009 at 07:02 AM.
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    V is a vectoric space.
    W_1,W_2\subseteq V\\
    W_1\nsubseteq W_2\\
    W_2\nsubseteq W_1\\
    prove that W_1 \cup W_2 is not a vectoric subspace of V.

    i dont ave the shread of idea on how to tackle it
    i only know to prove that some stuff is subspace
    but constant mutiplication
    and by sum of two coppies

    this question here differs a lot

    When you say you "have no idea how to tackle this" you run the risk someone will think you're trying to get somebody to do your hw for you, and that's something many of us won't accept to do.

    Try to understand well-well the definitions and the given data in your problem, and then try to understand the following rather good hint:

    As  W_1\nsubseteq W_2\,,\,\,\exists w_1\in W_1\setminus W_2 , and as  W_2\nsubseteq W_1\,,\,\,\exists w_2\in W_2\setminus W_1

    Get a contradiction now by showing that it is impossible that w_1+w_2\in W_1\cup W_2

    Tonio
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  3. #3
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    W_1 \ W_2 means complement by set theory

    wee need to add all the members which exist in W_2 who are not presented in W1
    so basically its
    <br />
W_1 \cup W_2<br />
    because there intersection is zero


    so i cant see a contradiction its very possible that w1+w2 is a part of
    <br />
W_1 \cup W_2<br />


    and i cant understand the meaning of w1+w2
    there is no such symbol in set theory

    ?
    Last edited by transgalactic; October 26th 2009 at 08:35 AM.
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  4. #4
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    Quote Originally Posted by transgalactic View Post
    W_1 \ W_2 means complement by set theory

    wee need to add all the members which exist in W_2 who are not presented in W1
    so basically its
    <br />
W_1 \cup W_2<br />
    because there intersection is zero


    so i cant see a contradiction its very possible that w1+w2 is a part of
    <br />
W_1 \cup W_2<br />


    and i cant understand the meaning of w1+w2
    there is no such symbol in set theory

    ?

    But we're talking about vector spaces and there's sum of vectors!

    Tonio
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  5. #5
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    aahh ok i agrree with you
    now i see its a sum of vectors

    so we have two groups of vectors they dont have common vectors

    if we sum both groups we get a new group of vectors
    which is lenear combination of both

    but what is the relations of this new group with

    <br />
W_1 \cup W_2<br />

    <br />
W_1 \cup W_2<br />
represents all the members from both groups
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  6. #6
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    i cant understand what w1+w2 group means

    we have two groups of vectors and we sum them

    how we some them?
    what is the meaning of w1+w2 in the ven diagram?
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  7. #7
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    Quote Originally Posted by transgalactic View Post
    i cant understand what w1+w2 group means

    we have two groups of vectors and we sum them

    how we some them?
    what is the meaning of w1+w2 in the ven diagram?

    Please do read again your definitions and THEN re-read and re-attack this problem. It is already solved but you can't tell since you don't understand the basics, which is something you must do by yourself.

    Tonio
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