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In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!" [2] or "∃ =1". For example, the formal statement
A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e. surjective). Not translatable (without circumlocutions) to some languages other than English.
There is an essentially unique two-dimensional, compact, simply connected manifold: the 2-sphere. In this case, it is unique up to homeomorphism. In the area of topology known as knot theory, there is an analogue of the fundamental theorem of arithmetic: the decomposition of a knot into a sum of prime knots is essentially unique. [5]
Unique primarily refers to: Uniqueness , a state or condition wherein something is unlike anything else In mathematics and logic, a unique object is the only object with a certain property, see Uniqueness quantification
The first solution with no prime number is the fourth which appears at X + Y ≤ 2522 or higher with values X = 16 = 2·2·2·2 and Y = 111 = 3·37. If the condition Y > X > 1 is changed to Y > X > 2, there is a unique solution for thresholds X + Y ≤ t for 124 < t < 5045, after which there are multiple solutions. At 124 and below, there are ...
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Initial and terminal objects are not required to exist in a given category. However, if they do exist, they are essentially unique. Specifically, if I 1 and I 2 are two different initial objects, then there is a unique isomorphism between them. Moreover, if I is an initial object then any object isomorphic to I is also an initial object. The ...
commutes and such that (P, i 1, i 2) is universal with respect to this diagram. That is, for any other such triple (Q, j 1, j 2) for which the following diagram commutes, there must exist a unique u : P → Q also making the diagram commute: As with all universal constructions, the pushout, if it exists, is unique up to a unique isomorphism.