I was given a question to find a bijection $f$ from $[0,1]$ into $(0,1)$.I have no idea of how to do this.Can any one please help me to solve this?
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Did you search for any similar questions? – Shoutre Nov 23 '15 at 00:58
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You've asked like three of the same questions. Can you please relax your pace? – Asaf Karagila Nov 23 '15 at 00:58
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The thing is im don't get how to solve these kind of sums for any given interval :( – Anupama Nov 23 '15 at 01:02
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They're both uncountable.
To map $[0,1] \rightarrow (0,1)$, try mapping $0 \mapsto \frac12$, $\frac1n \mapsto \frac1{n+2}$ for $n \in \mathbb N$, and use the identity everywhere else.
djechlin
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