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### Bijection between $[0,1]$ and $[0,1]\times[0,1]$ [duplicate]

I know that $|\mathbb R|=|\mathbb R\times\mathbb R|$, and that $|[0,1]|=|\mathbb R|$, which suggests that $|[0,1]|=|[0,1] \times [0,1]|$ but I would like to know a bijection between the interval and ...
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### Is $\mathbb R^2$ equipotent to $\mathbb R$? [duplicate]

I know that $\mathbb N^2$ is equipotent to $\mathbb N$ (By drawing zig-zag path to join all the points on xy-plane). Is this method available to prove $\mathbb R^2$ equipotent to $\mathbb R$?
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### Bijection from $[0,1]^3$ to $[0,1]$? [duplicate]

Is there any bijection from $[0,1]^3$ to $[0,1]$? How can I construct it?
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### How to Prove $\mathbb R\times \mathbb R \sim \mathbb R$? [duplicate]

How to prove $\mathbb R\times \mathbb R \sim \mathbb R$? I know you have to split the problem up into two claims, for each direction to prove that it is a bijection, but i don't know how to go much ...
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### Bijection from $\mathbb{R} \to \mathbb{R} \times \mathbb{R}$? [duplicate]

Possible Duplicate: bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ I know it's possible to produce a bijection from $\mathbb{Z}$ to $\mathbb{Z}\times\mathbb{Z}$, but is it possible to do ...
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### Elegant way to make a bijection from the set of the complex numbers to the set of the real numbers [duplicate]

Make a bijection that shows $|\mathbb C| = |\mathbb R|$ First I thought of dividing the complex numbers in the real parts and the complex parts and then define a formula that maps those parts to the ...
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### Bijection between $\mathbb{R}\times\mathbb{R}$ and $\mathbb{R}$ [duplicate]

It must be posted somewhere, but I can't find it. I've been working on it for a while too without getting anywhere. Does there exist a bijection between $\mathbb{R}\times\mathbb{R}$ and $\mathbb{R}$? ...