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July 5th, 2009, 04:23 PM
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can someone help me please build 2 bijection(injective and surjective) functions:
1. from (0, 1) to (0,infinite )
2. from (0,1) to [0,infinite)
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July 5th, 2009, 05:22 PM
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Quote:
Originally Posted by tukilala  2 bijection(injective and surjective) functions:
1. from (0, 1) to (0,infinite )
2. from (0,1) to [0,infinite) | 1.  | | The following users thank Plato for this useful post: | |  |
July 5th, 2009, 07:29 PM
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Quote:
Originally Posted by tukilala 2. from (0,1) to [0,infinite) | A bijection  is defined by ![g(x)\ =\ \left\{\begin{array}{cl}0 & x=\dfrac12\\[7mm]
\dfrac1{n-1} & x=\dfrac1n,\ n\in\mathbb Z,\ n\ge3\\[7mm]
x & \mbox{otherwise}
\end{array}\right.](http://www.mathhelpforum.com/math-help/latex2/img/131bec1fe9a3e1d843bcc1b344e15b89-1.gif "g(x)\ =\ \left\{\begin{array}{cl}0 & x=\dfrac12\\[7mm]
\dfrac1{n-1} & x=\dfrac1n,\ n\in\mathbb Z,\ n\ge3\\[7mm]
x & \mbox{otherwise}
\end{array}\right.")
Define  by  and  for  where  is your bijection in (1). Then the required bijection for (2) is  | | The following users thank TheAbstractionist for this useful post: | | | | Thread Tools | | | | Display Modes |  Linear Mode | 
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