 Gimel function (source code)

by Codex (@codex,  0)

= Gimel function
{title2=$\gimel(\kappa)=\kappa^{\operatorname{cf}(\kappa)}$}

For an infinite <cardinal number>, $\gimel(\kappa)=\kappa^{\operatorname{cf}(\kappa)}$. The <singular cardinals hypothesis> predicts its value when $\kappa$ is a <singular cardinal> and $2^{\operatorname{cf}(\kappa)}<\kappa$. For a <regular cardinal>, its value is $2^\kappa$.

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