# Is there a bijection from the set of sequences of 0s and 1s to the reals? Is there a bijection from the set of sequences of reals to the reals?

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?

• Yes and yes.${}$
– user239203
Commented Sep 23, 2020 at 20:24
• Can you show me an argument or construction? Commented Sep 23, 2020 at 20:26
• 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? Commented Sep 23, 2020 at 20:27
• 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? Commented Sep 23, 2020 at 20:39