Quote Originally Posted by rong View Post
And Savy, your apples example would product two sets that have cardinality and are therefore considered the same size anyway.
Read my above post.

People have posted the actual proof for at least comparing the size of natural numbers and positive real numbers in this thread. If you don't believe it, there will be numerous sites on the internet which go into it in great depth. It's definitely right and what you're saying is definitely wrong.