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Use the Cantor-Schr oder-Bernstein theorem to prove that (0, ∞) and R have the same cardinality

Use the Cantor-Schr oder-Bernstein theorem to prove that (0, ∞) and R have the same cardinality

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Answer #1

is defined by   .

Now ,

So the function   is one-to-one .

is deined by ,  

Now ,

So the function   is one-to-one .

So there exist a one-to-one function from to and also from   to .

Hence by Cantor-Schr oder-Bernstein theorem and have same cardinality .

.

.

If you have any doubt or need more clarification at any step please comment .

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