Quote Originally Posted by dancrilis View Post
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.
Yeah, like I said, it isn't intuitively logical.

It really doesn't matter that a bounded infinity includes other bounded infinities. Infinity x2 is exactly the same size as infinity cubed. They may include different components, but all infinities are equally infinite.

This is not the same as apples and oranges. If one has all the apples, and someone else has all the oranges, combining the two creates a greater whole. Combining two finite things does that.

Infinities are imaginary. They do not have limits such as all the apples or all the grains of sand on Earth, or even all the atoms currently existing in the universe. So no matter how infinite one's imagination, one can always imagine doubling the quantity or halving the granularity, or +1 more imaginary unit.

The quantity of any one infinity is the same as the quantity of any two infinities, or of every infinity combined. Infinity = infinity.