= Infinite percolation cluster
An infinite <percolation cluster> is an open <connected component of a graph> with infinitely many <graph vertices>. On a countable translation-invariant lattice, a zero root <percolation probability> implies that no <infinite percolation cluster> exists <almost surely>, by the countable union over all <graph vertices>. A positive root <probability> implies almost-sure existence by <translation ergodicity of Bernoulli percolation>; uniqueness is an additional theorem.
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