Prove that $ \mathbb{R}$ and the interval [0,1 ] have the same cardinality.

Question

I'm having troubles with a question.

Prove that $\mathbb{R}$ and the interval [0,1] have the same cardinality.

Can you help me, please?

Thank you in advance!

If $|[0,1]| \leq |\mathbb{R}|$ and $|[0,1]| \geq |\mathbb{R}|$ then their cardinalities are equal. One is trivial. Can you think of how to show the other? — AlphaNumeric, Nov 24 '16 at 11:29

score -3 · Answer 1 · answered Nov 24 '16 at 11:28

-3

Find a function $f: \mathbb R \to [0,1]$ which is bijective.

answered Nov 24 '16 at 11:28

Fred

We only need one-to-one function from $\mathbb R$ to $[0,1]$ because $[0,1]$ is a subset of $\mathbb R$. – MaliMish Nov 24 '16 at 11:32
might tan(πx+π/2) be the function that i should look for? – E.D. Nov 25 '16 at 12:20

1 Answers1