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Math Help - How to proof that a set is not empty?

  1. #1
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    How to proof that a set is not empty?

    Hi,

    how one can show that a set is not empty?

    I ask because I have to checking sets as they are vector subspaces and one of the rules for subspaces are that they are don't the empty set, but how to show that?

    Thanks
    greetings
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  2. #2
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    Quote Originally Posted by Herbststurm View Post
    how one can show that a set is not empty?
    That is an existential question. (I am not trying to be a smart off.) Itís true.
    Show that some element in the space must be in the set.
    Find some element which must belong to the set in question.
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  3. #3
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    Quote Originally Posted by Herbststurm View Post
    Hi,

    how one can show that a set is not empty?

    I ask because I have to checking sets as they are vector subspaces and one of the rules for subspaces are that they are don't the empty set, but how to show that?

    Thanks
    greetings
    In the case of vector subspaces, being non empty is equivalent to containing the zero element 0. So you should wonder if 0 is in your subspace. In at least 99.99% of the cases, this is obvious to check.
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  4. #4
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    Quote Originally Posted by Plato View Post
    That is an existential question. (I am not trying to be a smart off.) It’s true.
    Show that some element in the space must be in the set.
    Find some element which must belong to the set in question.
    I know that I have to find an element in the set which is not the empty set. I don't know how to find it. I have not a concrete set. The only thing which is given is that the set is a subset of a vector space.
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  5. #5
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    Zero has to be in a vector subspace by definition.
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  6. #6
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    hmm, yes but is this adequate for the proof? I mean it is clear that every set has as element the empty set but how to show that there are others which are not the empty set?

    The hole problem is that I don't have a specified set. I only have:

    Let U be a subset of a vector space. Ist the set a times U a vector subspace? a are elements of a field.

    I have no concrete things.
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