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:
“Children need money. As they grow older they need more money. They need money for essentially the same reasons that adults need money. They need to buy stuff....They need it regardless of whether they get good grades, violate a family rule, or offend a parent.”
—Donald C. Medeiros (20th century)
“I think it’s unfair for people to try to make successful blacks feel guilty for not feeling guilty.... We’re unique in that we’re not supposed to enjoy the things we’ve worked so hard for.”
—Patricia Grayson, African American administrator. As quoted in Time magazine, p. 59 (March 13, 1989)