In mathematics, the term essentially unique is used to indicate that while some object is not the only one that satisfies certain properties, all such objects are "the same" in some sense appropriate to the circumstances. This notion of "sameness" is often formalized using an equivalence relation.
A related notion is a universal property, where an object is not only essentially unique, but unique up to a unique isomorphism (meaning that it has trivial automorphism group). In general given two isomorphic examples of an essentially unique object, there is no natural (unique) isomorphism between them.
Famous quotes containing the words essentially and/or unique:
“We find ourselves under the government of a system of political institutions, conducing more essentially to the ends of civil and religious liberty, than any of which the history of former times tells us.”
—Abraham Lincoln (1809–1865)
“At this unique distance from isolation
It becomes still more difficult to find
Words at once true and kind,
Or not untrue and not unkind.”
—Philip Larkin (1922–1986)