I believe the continuum hypothesis is an example of an undecidable statement. That is, we know that the integers have cardinality of “aleph null”, the smallest

I believe the continuum hypothesis is an example of an undecidable statement. That is, we know that the integers have cardinality of “aleph null”, the smallest infinity. And we know how to construct the “next” level of infinity using something analogous to power sets. Call this “aleph one”. Now the hypothesis: the cardinality of the real numbers is equal to aleph one. It is known that we can never prove that hypothesis one way or the other. The US mathematician Paul Cohen established this in the 1960s. There are probably egregious errors in my telling of this, but it could be a prompt for further reading.