Mathematical concept for comparing objects
Transitive binary relations
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Y indicates that the column's property is always true the row's term (at the very left), while ✗ indicates that the property is not guaranteed in general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively.
All definitions tacitly require the homogeneous relation be transitive: for all if and then
A term's definition may require additional properties that are not listed in this table.
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In mathematics, specifically order theory, a well-quasi-ordering or wqo on a set
is a quasi-ordering of
for which every infinite sequence of elements
from
contains an increasing pair
with