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Thread: Notation question

  1. #1
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    Notation question

    Hey,

    I would like to prove that $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ is uncountable. My first question is what the notation $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ means precisely (I am not familiar with the notation).
    I am only asking someone to clarify the notation and NOT to help with the proof (I would like to have a crack at it myself and then return if I get stuck).

    Thanks.
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  2. #2
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    Re: Notation question

    Quote Originally Posted by detalosi View Post
    Hey,

    I would like to prove that $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ is uncountable. My first question is what the notation $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ means precisely (I am not familiar with the notation).
    I am only asking someone to clarify the notation and NOT to help with the proof (I would like to have a crack at it myself and then return if I get stuck).
    If each of $A~\&~B$ is a set then $B^A$ stands for the set of all functions from $A$ to $B$.

    In this case $\displaystyle \left\{0,1\right\}^{\mathbb{N}}$ is the set of all bit-strings. That is the set of all sequences with only 0's & 1's as entries.
    Thanks from detalosi, topsquark and HallsofIvy
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