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...

uniqueness is "uniqueness up to equality"). This is called essentially unique. For example, many concepts in category theory are defined to be unique...

series Glee All pages with titles beginning with Unique Essentially unique Sui generis The Uniques (disambiguation) Uniq (disambiguation) This disambiguation...

Uniqueness case in finite group theory. The word unique is sometimes replaced by essentially unique, whenever one wants to stress that the uniqueness...

} The rings in which factorization into irreducibles is essentially unique are called unique factorization domains. Important examples are polynomial...

subgroups of Lie groups are not in general unique, but are unique up to conjugation – they are essentially unique. An example would be the subgroup O(2),...

polynomials, such as the essentially unique factorization into prime or irreducible factors. When the coefficient ring is a field or other unique factorization domain...

pullback of two morphisms f and g need not exist, but if it does, it is essentially uniquely defined by the two morphisms. In many situations, X ×Z Y may intuitively...

group. These manifolds are uniquely determined by their fundamental groups. They can all be represented in an essentially unique way as Seifert fiber spaces:...

any positive integer can be written as the products of primes in an essentially unique way. This is the fundamental theorem of arithmetic. Z {\displaystyle...

Aadhaar (Hindi: आधार, lit. 'base, foundation') is a twelve-digit unique identity number that can be obtained voluntarily by all residents of India, based...

an initial segment of the other. So ordinal numbers exist and are essentially unique. Ordinal numbers are distinct from cardinal numbers, which measure...

{\displaystyle (A,u)} does exist, then it is essentially unique. Specifically, it is unique up to a unique isomorphism: if ( A ′ , u ′ ) {\displaystyle...

they do exist, they are essentially unique. Specifically, if I1 and I2 are two different initial objects, then there is a unique isomorphism between them...

one might express this by saying that the smooth structure is (essentially) unique. The case for k = 0 is different. Namely, there exist topological...

set for μ {\displaystyle \mu } . Moreover, this decomposition is essentially unique, meaning that for any other pair ( P ′ , N ′ ) {\displaystyle (P'...

projective 3-space P3. It is a fundamental example of a skew curve. It is essentially unique, up to projective transformation (the twisted cubic, therefore). In...

is essentially self-adjoint if it has a unique self-adjoint extension. In practical terms, having an essentially self-adjoint operator is almost as good...

computation. The work of Gödel showed that the notion of computation is essentially unique. In 1941 Konrad Zuse completed the Z3 computer. Zuse was not familiar...

dimension 3, Edwin E. Moise proved that every topological manifold has an essentially unique smooth structure (see Moise's theorem), so the monoid of smooth structures...

set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion, which is a complete Boolean algebra containing A such...

isolation is the subjective feeling that every human life experience is essentially unique and can be understood only by themselves, creating a gap between a...

relationship between male euglossine bees and volatile chemicals is essentially unique in the animal kingdom. Scientists use single synthetic compounds as...

is almost never unique (the counterexamples are trivial); see below. A complete flag on an inner product space has an essentially unique orthonormal basis:...

in Wiktionary, the free dictionary. Abuse of notation Adequality Essentially unique List of mathematical jargon Modulo (jargon) Quotient group Quotient...

rather than played in an actual game—where the goal is to find the essentially unique way for one side (usually White) to win or draw, as stipulated, against...

composed of only 1 cell) and n = 3. Moreover, the solution of order 3 is essentially unique. Meng gives a less intricate constructive proof. The order-3 magic...

cyclic shifts". Look up modulo in Wiktionary, the free dictionary. Essentially unique List of mathematical jargon Up to "Modular arithmetic". Encyclopedia...

can be written as a connected sum of prime homology 3-spheres in an essentially unique way. (See Prime decomposition (3-manifold).) Suppose that a 1 , …...

tensor A {\displaystyle {\mathcal {A}}} are called identifiable or essentially unique. A rank- r {\displaystyle r} tensor A ∈ F I 1 ⊗ F I 2 ⊗ ⋯ ⊗ F I M...