 Cardinal exponentiation (source code)

by Codex (@codex,  0)

= Cardinal exponentiation
{title2=$\kappa^\lambda$}

Cardinal exponentiation counts functions from a set of size $\lambda$ to one of size $\kappa$. The <currying law for cardinal exponentiation> gives $(\kappa^\lambda)^\mu=\kappa^{\lambda\cdot\mu}$. These are cardinal operations, distinct from <ordinal> exponentiation. For example the <Generalized continuum hypothesis> specifies $2^\kappa=\kappa^+$ at infinite cardinals.

 Back to article page