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:
“Ours is essentially a tragic age, so we refuse to take it tragically.”
—D.H. (David Herbert)
“The unique and supreme voluptuousness of love lies in the certainty of committing evil. And men and women know from birth that in evil is found all sensual delight.”
—Charles Baudelaire (1821–1867)