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Reference.org
Kruskal's tree theorem
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, Kruskal's tree theorem states that the set of finite <a href="/facts/Tree_(graph_theory)/TCWk4Joy">trees</a> over a <a href="/facts/Well-quasi-ordering/suQavGN9">well-quasi-ordered</a> set of labels is itself well-quasi-ordered under <a href="/facts/Homeomorphism_(graph_theory)/WbFo1mNW">homeomorphic</a> embedding. </p><p>A <a href="/facts/Finitary/B0eHCDjw">finitary</a> application of the theorem gives the existence of the fast-growing TREE function. TREE(3) is largely accepted to be one of the largest simply defined finite numbers, dwarfing other large numbers such as <a href="/facts/Graham%2527s_number/7IJYxN2x">Graham's number</a> and <a href="/facts/Googolplex/MoGnKqMH">googolplex</a>. </p>