Concept

# Essentially unique

Summary
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. 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 there can be more than one isomorphism between examples of an essentially unique object. Examples Set theory At the most basic level, there is an essentially unique set of any given cardinality, whether one labels the elements {1,2,3} or {a,b,c}. In this case, the non-uniqueness of the isomorphism (e.g., match 1 to a or 1 to c) is reflected in the symmetric group. On the
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