The article asks, how can infinite come in many sizes, and then proceeds to list just two sizes: \aleph_0 and 2^{\aleph_0}.
If you are interested in this, you can choose to study (1) why is the set of real numbers the same size as the powerset of the natural numbers; (2) why is any set (infinite or not) smaller in size than its powerset; (3) doing arithmetic on sizes of sets, for example what it means to have one more than the size of the natural numbers or twice the size of the natural numbers; (4) the continuum hypothesis, that there is no set bigger than the natural numbers and smaller than the real numbers.
Unfortunately there’s not much else about cardinal numbers that beginners can readily grasp; you’ll have to switch your study to ordinal numbers.
The article asks, how can infinite come in many sizes, and then proceeds to list just two sizes: \aleph_0 and 2^{\aleph_0}.
If you are interested in this, you can choose to study (1) why is the set of real numbers the same size as the powerset of the natural numbers; (2) why is any set (infinite or not) smaller in size than its powerset; (3) doing arithmetic on sizes of sets, for example what it means to have one more than the size of the natural numbers or twice the size of the natural numbers; (4) the continuum hypothesis, that there is no set bigger than the natural numbers and smaller than the real numbers.
Unfortunately there’s not much else about cardinal numbers that beginners can readily grasp; you’ll have to switch your study to ordinal numbers.