In contrast, cardinal exponentiation is highly non-trivial, for even the value of the simplest non-trivial infinite exponential, namely \(2^{\aleph_0}\), is not known and cannot be determined in ZFC (see below). The cardinal \(\kappa^\lambda\) is defined as the cardinality of the Cartesian product of \(\lambda\) copies of \(\kappa\); equivalently, as the cardinality of the set of all functions from \(\lambda\) into \(\kappa\). König’s theorem asserts that \(\kappa^{cf(\kappa)}&gt;\kappa\), which implies that the cofinality of the cardinal \(2^{\aleph_0}\), whatever that cardinal is, must be uncountable. But this is essentially all that ZFC can prove about the value of the exponential \(2^{\aleph_0}\).