this post was submitted on 27 Feb 2024
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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.