Zhen Chanzi's Journey to Seek His Roots

The first of Hilbert's Twenty-Three Questions: the problem of the cardinality of the continuum.

The continuum problem was the question of whether there existed no cardinality between that of a countable set and that of the set of real numbers.

So-called "cardinality" referred to the "absolute measure" of a set. If a set contained one element, its cardinality was one; if it contained two elements, its cardinality was two. And so on.

As for infinitely countable sets such as "all integers" and "all natural numbers," their cardinality was denoted as "Aleph-null"—known in the Divine Land as the "Dao Yuan Zero Number," the smallest infinite integer.

The ancients of the Divine Land had once believed that the totality of numbers, infinitely vast, was the number of the Dao.

Aleph-null plus one was still Aleph-null. Aleph-null plus Aleph-null was still Aleph-null. Aleph-null times Aleph-null was still Aleph-null.

Infinite magnitude, positive infinity. Ordinary operations carried no meaning whatsoever for this number.

Then were there numbers greater than this infinite number in the world?

In fact, there were.

They were the cardinalities of "power sets."

If a set had the single element "1," then its power set had two members—"1" and the empty set.

If a set had the two elements "1, 2," then it had four power sets—the empty set, the set {1}, the set {2}, and the set {1, 2}.

And so on. When a set had three elements, it had eight power sets. When the number of elements rose to four, the power set rose to sixteen.

A set's power set always had more elements than the set itself. If a set had N elements, then it had 2 to the Nth power power sets.

The power set of an infinitely countable set, two to the Aleph-null power, was the second