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:
“Dream is not a revelation. If a dream affords the dreamer some light on himself, it is not the person with closed eyes who makes the discovery but the person with open eyes lucid enough to fit thoughts together. Dream—a scintillating mirage surrounded by shadows—is essentially poetry.”
—Michel Leiris (1901–1990)
“... a unique endeavour
To bring to bloom the million-petalled flower
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