They’re both countable, which makes them both the same size. When you say two infinities are the same size, what you’re saying is that there exists a 1:1 mapping to go from one to the other.
In your proposed case every integer maps directly onto the even number twice its size.
They’re both countable, which makes them both the same size. When you say two infinities are the same size, what you’re saying is that there exists a 1:1 mapping to go from one to the other.
In your proposed case every integer maps directly onto the even number twice its size.