@clousems a better example of different sizes of infinity imo is the cardinality of Z vs R because one can show that Z is countably infinite while R is uncountably infinite
#21
Transfinite numbers, the ladder of alephs
aleph0 = #N = #Z = #Q = number of counting numbers
aleph1 = aleph0^2
aleph2 = aleph1^2
aleph3 = aleph2^2
aleph4 = aleph3^2
There is not even proof that
aleph1 = #R = #C = #R^3 = number of points in space
Likewise
aleph2 = number of possible curves on a postage stamp, number of possible statues, number of possible paintings
aleph3 = beyond human imagination
