equivalence relation
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An equivalence relation is a way of connecting things together that follows three basic rules: everything relates to itself (reflexive), if one thing relates to another then the reverse is true (symmetric), and if one thing relates to a second and the second relates to a third, then the first relates to the third (transitive). This concept matters because it lets mathematicians and logicians organize things into groups where members are considered "equivalent" in some meaningful way.
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Y indicates that the column's property is always true for 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
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