A beth number is a member of the sequence of infinite cardinals indexed by ordinals,
starting with 
and continuing by 
at a successor ordinal and 
at a nonzero
limit ordinal. Cardinal
exponentiation here gives the cardinality
of a power set.
Thus 
is the cardinality
of the continuum. Under the continuum hypothesis,
, so the ordinal
used to index 
is 
. This prescribed threshold occurs
in one formulation of the eventual
categoricity conjecture for abstract
elementary classes.
