Quote Originally Posted by brian 333 View Post
Logically this appears to be true.

It is not.

Infinity is not logical to minds that have trouble counting past 20. But the entire infinity of numbers, (a bounded infinity because it excludes everything except numbers,) can be divided exactly the same number of times as the infinity between 2 and 3.

Infinity = infinity
There are an infinite amount of numbers between 1 and 2, and there are also an infinite amount of numbers between 1 and 3.

That second infinity encompasses the first and also has extra - they are not the same size.