equivalent

1. (mathematics) Of two sets, having a one-to-one correspondence.Examples: "Finite sets A and B are equivalent sets only when n(A) = n(B) i.e., the number of elements in A and B are equal."; "All enumerable sets are equivalent to each other, but not to any finite set."; "Equivalent sets should, by rights, have the same "number" of elements. For this reason we sometimes say that equivalent sets have the same cardinality."Synonyms: equinumerous

2. (mathematics) Relating to the corresponding elements of an equivalence relation.

3. (mathematics, category theory) Of two categories, (informally) such that one is essentially a relabeling of the other; (formally) related by a pair of functors such the composition of the one with the other is naturally isomorphic to the identity functor.

4. (chemistry) Having the equal ability to combine.

5. (cartography) Of a map, equal-area.

6. (geometry) Equal in measure but not admitting of superposition; applied to magnitudes.Examples: "A square may be equivalent to a triangle."