 This means that, for every set formula_2 of cardinality formula_3, and every partition of the ordered pairs of elements of formula_2 into two subsets formula_5 and formula_5, there exists either a subset formula_7 of cardinality formula_3 or a subset formula_9 of cardinality formula_10, such that all pairs of elements of formula_11 belong to formula_12.Here, formula_5 can be interpreted as the edges of a graph having formula_2 as its vertex set, in which formula_15 (if it exists) is a clique of cardinality formula_3, and formula_17 (if it exists) is a countably infinite independent set.If formula_2 is taken to be the cardinal number formula_3 itself, the theorem can be formulated in terms of ordinal numbers with the notation formula_20, meaning that formula_17 (when it exists) has order type formula_22.