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Reference.org
Tree (set theory)
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<p>In <a href="/facts/Set_theory/1ptfsvUP">set theory</a>, a tree is a <a href="/facts/Partially_ordered_set/qb4a3FAX">partially ordered set</a> ( T , < ) {\displaystyle (T,<)} such that for each t ∈ T {\displaystyle t\in T} , the set { s ∈ T : s < t } {\displaystyle \{s\in T:s<t\}} is <a href="/facts/Well-ordered/GrWEBWlW">well-ordered</a> by the relation < {\displaystyle <} . Frequently trees are assumed to have only one root (i.e. <a href="/facts/Minimal_element/7FCC9qAW">minimal element</a>), as the typical questions investigated in this field are easily reduced to questions about single-rooted trees. </p>