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  2. Picard–Lindelöf theorem - Wikipedia

    en.wikipedia.org/wiki/Picard–Lindelöf_theorem

    A standard proof relies on transforming the differential equation into an integral equation, then applying the Banach fixed-point theorem to prove the existence of a solution, and then applying Grönwall's lemma to prove the uniqueness of the solution.

  3. Uniqueness quantification - Wikipedia

    en.wikipedia.org/wiki/Uniqueness_quantification

    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.

  4. Uniqueness theorem - Wikipedia

    en.wikipedia.org/wiki/Uniqueness_theorem

    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]

  5. Cauchy–Kovalevskaya theorem - Wikipedia

    en.wikipedia.org/wiki/Cauchy–Kovalevskaya_theorem

    In mathematics, the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems. A special case was proven by Augustin Cauchy , and the full result by Sofya Kovalevskaya .

  6. Disjunction and existence properties - Wikipedia

    en.wikipedia.org/wiki/Disjunction_and_existence...

    The disjunction property is satisfied by a theory if, whenever a sentence A ∨ B is a theorem, then either A is a theorem, or B is a theorem.; The existence property or witness property is satisfied by a theory if, whenever a sentence (∃x)A(x) is a theorem, where A(x) has no other free variables, then there is some term t such that the theory proves A(t).

  7. Existence theorem - Wikipedia

    en.wikipedia.org/wiki/Existence_theorem

    Despite that, the purely theoretical existence results are nevertheless ubiquitous in contemporary mathematics. For example, John Nash's original proof of the existence of a Nash equilibrium in 1951 was such an existence theorem. An approach which is constructive was also later found in 1962. [6]

  8. California gave drivers a new option for gender on their IDs ...

    www.aol.com/news/california-gave-drivers-option...

    Four years after California began issuing nonbinary IDs, fewer than 16,000 people have asked the state for a little piece of plastic with their gender marked by an X rather than an F or M.

  9. Gödel's ontological proof - Wikipedia

    en.wikipedia.org/wiki/Gödel's_ontological_proof

    Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109).