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Is there a bijection from the set of sequences of 0s and 1s to the reals? I believe this is true since every real number cab be represented as a binary. But I do not know how to do so.

Is there a bijection from the set of sequences of reals to the reals? Could this just be placing each digit of the unique decimal representation of a number into a sequence and vice versa?

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  • $\begingroup$ Yes and yes.${}$ $\endgroup$
    – user239203
    Commented Sep 23, 2020 at 20:24
  • $\begingroup$ Can you show me an argument or construction? $\endgroup$
    – E2R0NS
    Commented Sep 23, 2020 at 20:26
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    $\begingroup$ From the dialog that appeared when you clicked "Ask Question: "2. Provide details and any research 3. When appropriate, describe what you’ve tried". Can you show any research or describe what you've tried? $\endgroup$
    – Eric Towers
    Commented Sep 23, 2020 at 20:27
  • $\begingroup$ For bijection you need to show that works both ways. For example, in the first case, can any sequence of $0$ and $1$ be a real? Or in the second case, if you have a sequence of reals, say $\{e,\pi,\sqrt 2\}$, how would you represent it as a unique real number? $\endgroup$
    – Andrei
    Commented Sep 23, 2020 at 20:39

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