Is every real number the smallest infinity? Would the infinity of every even number be smaller than the infinity of every integer? Or are they both aleph-null?
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.
Is every real number the smallest infinity? Would the infinity of every even number be smaller than the infinity of every integer? Or are they both aleph-null?
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.