[zafxfarf] Constants among higher transfinities

Among the set of integers, which has cardinality aleph-null, there are some interesting constants, for example, 1729.

For the sake of brevity, assume the continuum hypothesis.

Among the real numbers, which has cardinality aleph-one, there are some interesting constants, for example, pi.

If we continue the sequence, what interesting constants exist within sets of higher transfinite cardinalities?

Among the set of functions, which has cardinality aleph-two, some such constants could be interesting geometric shapes. Among the power set of functions, which has cardinality aleph-three, some such constants could be interesting families of functions.

But I can't shake the feeling that the real constants are somehow more interesting than the constants from other sets.