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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]
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.
which completes the proof that 3 is the unique solution of + =. In general, both existence (there exists at least one object) and uniqueness (there exists at most one object) must be proven, in order to conclude that there exists exactly one object satisfying a said condition.
Not every law school graduate passes the California bar exam; its 2024 failure rate was 44 percent. The precocious siblings, purposely left unnamed, cannot be faulted for their remarkable ...
Following graduation, Witkin took a job with a law firm in San Francisco for two years, while continuing to develop and sell his outlines. Following that job, Witkin clerked for the California Supreme Court. At the same time, he started to teach a bar review course. [2] Witkin later clerked for the Chief Justice of the California Supreme Court.
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 ...
Rumors that San Luis Obispo County school districts are placing litter boxes in restrooms to accommodate students who identify as “furries” are false, school district administrators say.
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