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Math Help - Bijection

  1. #1
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    Bijection

    Hey all,

    I know there's a bijection between \mathbb{R} and \rbrack0,1\lbrack, but I was wondering if there was one between \mathbb{R}\ \mathbb{Q} and \mathbb{R}\ \mathbb{Q}\bigcap \rbrack0,1\lbrack.

    Can anyone help me? Thank you!
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  2. #2
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    What do you mean by \mathbb{R}/\mathbb{Q} because that is used to represent a factor ring but the problem is that \mathbb{Q} is not an indeal in \mathbb{R}. Thus you mean something else by the symbol / but I do not know what you mean.
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  3. #3
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    Sorry for the confusion, the backslash would mean, in this case, \mathbb{R} without \mathbb{Q}, or in other words the irrationals. Indeed, I am not trying to represent a factor ring.
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  4. #4
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    Quote Originally Posted by juef
    Sorry for the confusion, the backslash would mean, in this case, \mathbb{R} without \mathbb{Q}, or in other words the irrationals. Indeed, I am not trying to represent a factor ring.
    But the cardinality of the irrationals must be the countinuum. Because the cardinality of the rationals is \aleph_0.
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