Bijection

Calculus Level 3

True or false :

\quad There exists a bijection between [ 0 , 1 ] \left[ 0,1 \right] and ( 0 , 1 ) \left( 0,1 \right) .

True False

Ting Sie Kim by Ting Sie Kim , 27, Malaysia

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1 solution

Otto Bretscher
Mar 17, 2016

Let f ( 1 2 ± 1 2 n ) = 1 2 ± 1 2 ( n + 1 ) f\left(\frac{1}{2}\pm\frac{1}{2n}\right)=\frac{1}{2}\pm \frac{1}{2(n+1)} for positive integers n n and f ( x ) = x f(x)=x otherwise.

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