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

[MathMajor]

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.

Homework Equations

The Attempt at a Solution

 

[VeeEight]

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