In mathematics, the term essentially unique is used to describe a weaker form of uniqueness, where an object satisfying a property is "unique" only in the sense that all objects satisfying the property are equivalent to each other.
The notion of essential uniqueness presupposes some form of "sameness", which is often formalized using an equivalence relation.
In general there can be more than one isomorphism between examples of an essentially unique object.
At the most basic level, there is an essentially unique set of any given cardinality, whether one labels the elements
The fundamental theorem of arithmetic establishes that the factorization of any positive integer into prime numbers is essentially unique, i.e., unique up to the ordering of the prime factors.
In fact, regardless of how one chooses to write the three elements and denote the group operation, all such groups can be shown to be isomorphic to each other, and hence are "the same".
[4] There is an essentially unique measure that is translation-invariant, strictly positive and locally finite on the real line.
There is an essentially unique two-dimensional, compact, simply connected manifold: the 2-sphere.
[6] Given the task of using 24-bit words to store 12 bits of information in such a way that 4-bit errors can be detected and 3-bit errors can be corrected, the solution is essentially unique: the extended binary Golay code.