Cardinality

Referencing How Infinity Works (And How It Breaks Math) - YouTube

def. ${\beth }_0$ is the cardinality of natural numbers def. ${\beth }_1$ is the cardinality of real numbers

• ${\beth }_{n+1}=2^{{\beth }_n}$ i.e. ${\beth }_{n+1}$ is the cardinality of all the subsets of ${\beth }_n$

Continuum Hypothesis §

hyp. There is no set whose cardinality is between that of integers and real numbers.

• Expressed using above notation: ${\beth }_1\stackrel{?}{=}{\aleph }_1$
• This hypothesis is proved to be unprovable within ZFC, according to Limits of Math and Computing