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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
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
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]
A reference to a standard or choice-free presentation of some mathematical object (e.g., canonical map, canonical form, or canonical ordering). The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes.
A uniqueness theorem (or its proof) is, at least within the mathematics of differential equations, often combined with an existence theorem (or its proof) to a combined existence and uniqueness theorem (e.g., existence and uniqueness of solution to first-order differential equations with boundary condition). [3]
Get ready for all of today's NYT 'Connections’ hints and answers for #552 on Saturday, December 14, 2024. Today's NYT Connections puzzle for Saturday, December 14, 2024 The New York Times
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Similarly, the empty space is the unique initial object in Top, the category of topological spaces and every one-point space is a terminal object in this category. In the category Rel of sets and relations, the empty set is the unique initial object, the unique terminal object, and hence the unique zero object. Morphisms of pointed sets.