At the end of wolfram article on non-Archimedean valuation, it is claimed that the residual field of a complete non-Archimedean field is finite. This article does not have compactness assumptions on $K$ or $\mathcal{O}_K$.
In Proposition 27, p. 17 of a notes on valued fields, it claims that the ring of integers is compact if and only if residual field is finite.
Is compactness condition missing in the wolfram article? Is there an example of a complete non-Archimedean field with infinite residual field?