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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
This theorem is about the existence of solutions to a system of m differential equations in n dimensions when the coefficients are analytic functions. The theorem and its proof are valid for analytic functions of either real or complex variables. Let K denote either the fields of real or complex numbers, and let V = K m and W = K n.
Electromagnetism uniqueness theorem for the solution of Maxwell's equation. Uniqueness case in finite group theory. The word unique is sometimes replaced by essentially unique, whenever one wants to stress that the uniqueness is only referred to the underlying structure, whereas the form may vary in all ways that do not affect the mathematical ...
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.
From the other direction, there has been considerable clarification of what constructive mathematics is—without the emergence of a 'master theory'. For example, according to Errett Bishop's definitions, the continuity of a function such as sin(x) should be proved as a constructive bound on the modulus of continuity, meaning that the existential content of the assertion of continuity is a ...
The Employment Development Department is unveiling a newly updated and simplified unemployment benefit application that makes it easier to file. California's new application for unemployment ...
California’s unemployment remains the highest state rate in the nation. New data from the state’s Employment Development Department put the April rate at 5.3% for the third consecutive month.
Uniqueness: no positive integer n has two different Zeckendorf representations. The first part of Zeckendorf's theorem (existence) can be proven by induction . For n = 1, 2, 3 it is clearly true (as these are Fibonacci numbers), for n = 4 we have 4 = 3 + 1 .
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