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> Show $(a, b)$ has the same cardinality as $R$ for any interval $(a, b)$.
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From the previous chapters of the book (Understanding Analysis-Stephen Abbott), I know that $(-1,1)$ has the same cardinality as $R$. I am willing to know is there any systematic way to show this or I have to guess some function $f: (a,b)$ ->$(-1,1)$ that is 1-to-1 and onto?