Proving Equivalence of Sets - One-to-One and Onto Function

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Homework Statement


Hi, new to the Physics Forum and desperately need some help with a math analysis problem...

Prove that {x|x>1} and {x|0<x<1} are equivalent sets by writing a function and show that it is one-to-one and onto.


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The Attempt at a Solution

 
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The sets are not equivalent, rather they have the same cardinality.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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