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Math Help - Cardinality of sets Q and R

  1. #1
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    Cardinality of sets Q and R

    Hello all,

    I need your help for this one , thanks :

    prove that , the dimension between \mathbb{Q} and \mathbb{R} is infinite.
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  2. #2
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    Quote Originally Posted by linda2005 View Post
    prove that , the dimension between \mathbb{Q} and \mathbb{R} is infinite.
    Please repost the exact wording of the question.
    The above us not meaningful.
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  3. #3
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    I mean:
    the dimension of \mathbb {R} as \,\mathbb {Q}-vector\, spaces\; is infinite.
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  4. #4
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    Quote Originally Posted by linda2005 View Post
    I mean:
    the dimension of \mathbb {R} as \,\mathbb {Q}-vector\, spaces\; is infinite.
    that's trivial because a finite dimensional vector space over a countable field is countable but \mathbb{R} is uncountable.
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