Idempotent ultrafilter on the natural numbers
= Idempotent ultrafilter on the natural numbers
An ultrafilter $\mathcal U\in\beta\mathbb N$ is idempotent when $\mathcal U+\mathcal U=\mathcal U$. The <Ellis–Numakura lemma> guarantees such an ultrafilter and supplies the main algebraic input to the <Idempotent-ultrafilter proof of Hindman's theorem>.