Synonymer & Anagrammer | engelsk ord PROOF

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Eksempler på brug af PROOF i en sætning

• Automated reasoning over mathematical proof was a major motivating factor for the development of computer science.
• Conditional proof, in logic: a proof that asserts a conditional, and proves that the antecedent leads to the consequent.
• In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof.
• A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent.
• The proof consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004.
• Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination.
• Natural deduction, a class of proof systems based on simple and self-evident rules of inference that aim to closely mirror how reasoning actually occurs.
• Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).
• In propositional logic, disjunction elimination (sometimes named proof by cases, case analysis, or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.
• Traditionally, the sword in the stone that is the proof of Arthur's lineage and the sword given to him by a Lady of the Lake are not the same weapon, even as in some versions of the legend both of them share the name of Excalibur.
• He made the assertion known as Waring's problem without proof in his writings Meditationes Algebraicae.
• Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand.
• According to the Merriam-Webster's Dictionary, faith has multiple definitions, including "something that is believed especially with strong conviction", "complete trust", "belief and trust in and loyalty to God", as well as "a firm belief in something for which there is no proof".
• Dyson originated several concepts that bear his name, such as Dyson's transform, a fundamental technique in additive number theory, which he developed as part of his proof of Mann's theorem; the Dyson tree, a hypothetical genetically engineered plant capable of growing in a comet; the Dyson series, a perturbative series where each term is represented by Feynman diagrams; the Dyson sphere, a thought experiment that attempts to explain how a space-faring civilization would meet its energy requirements with a hypothetical megastructure that completely encompasses a star and captures a large percentage of its power output; and Dyson's eternal intelligence, a means by which an immortal society of intelligent beings in an open universe could escape the prospect of the heat death of the universe by extending subjective time to infinity while expending only a finite amount of energy.
• Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God.
• The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms.
• The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an article in 1930, titled "The completeness of the axioms of the functional calculus of logic" (in German)) is not easy to read today; it uses concepts and formalisms that are no longer used and terminology that is often obscure.
• It is a summons with the force of a court order; it is addressed to the custodian (a prison official, for example) and demands that a prisoner be brought before the court, and that the custodian present proof of authority, allowing the court to determine whether the custodian has lawful authority to detain the prisoner.
• It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves.
• Gödel's discoveries in the foundations of mathematics led to the proof of his completeness theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two years later, in 1931.

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