Wow this bafffles the mind. Consider the set of numbers x=1,2,3,4,etc and y=2,4,6,8,etc.. both sets are infinite in size right? But you can turn set x into set y by the function f(x)=2x right? So consider set x=1,2,3,4,5, etc and set y= all the numbers between 0 and 1. Both sets have...