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Spreadsheet 2000, S2K for short, featured a unique way of building complex spreadsheets from a number of simpler ones containing only input or output data. This contrasts with the traditional spreadsheet model, where inputs, calculations and outputs are all placed into a single sheet and cannot be easily differentiated.
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
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]
Comma- and space-separated formats often suffer from this problem, since in many contexts those characters are legitimate parts of a data field. Most such files avoid delimiter collision either by surrounding all data fields in double quotes, or only quoting those data fields that contain the delimiter character.
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
This completes the proof that there is the unique solution up to an additive constant of Poisson's equation with a Neumann boundary condition. Mixed boundary conditions could be given as long as either the gradient or the potential is specified at each point of the boundary. Boundary conditions at infinity also hold.
In relational database management systems, a unique key is a candidate key. All the candidate keys of a relation can uniquely identify the records of the relation, but only one of them is used as the primary key of the relation. The remaining candidate keys are called unique keys because they can uniquely identify a record in a relation.
The Peano existence theorem shows only existence, not uniqueness, but it assumes only that f is continuous in y, instead of Lipschitz continuous. For example, the right-hand side of the equation dy / dt = y 1 / 3 with initial condition y(0) = 0 is continuous but not Lipschitz continuous.