Examples of the the word, proof , in a Sentence Context

The word ( proof ), is the 2215 most frequently used in English word vocabulary

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  1. Or fourth century AD. The text may be as old as the first century, but other, proof ,of age has not been found. In a similar vein, the disciples of the Gnostic
  2. Brisbane prevents American relief of the Siege of Fort Steinway. *1787 – Sixty, proof ,sheets of the Constitution of the United States are delivered to the
  3. These theorems may not hold for mathematical objects of large cardinality. The, proof ,of the independence result also shows that a wide class of mathematical
  4. Algorithmically whether a given Turing machine will ever halt. While his, proof ,was published after Alonzo Church's equivalent proof in respect to his
  5. To the apostolic age, and universal acceptance by the church was required as, proof ,of apostolic authorship. As these principles gained currency, books deemed
  6. Proof, the word“ algebraic” is replaced by the word“ finite ”, then the, proof ,is still valid. Every endomorphic of FN has some eigenvector The field F is
  7. 12 November),Turing reformulated Kurt Gödel's 1931 results on the limits of, proof ,and computation, replacing Gödel's universal arithmetic-based formal language
  8. And he quoted his description of the armor adorning the walls of his house as, proof ,that he could be unusually warlike for a lyric poet. Other examples of his
  9. The paper and make a yes-no decision about the next instruction. Alan Turing's, proof ,of that the Entscheidungsproblem was unsolvable by use of his" an- automatic-
  10. Halt. While his proof was published after Alonzo Church's equivalent, proof ,in respect to his lambda calculus, Turing was unaware of Church's work at the
  11. Carmelo initially introduced the axiom of choice in order to formalize his, proof ,of the well-ordering theorem. **Well-ordering theorem: Every set can be
  12. Forall x \phi \to \fix_t is valid, that is, we must be able to give a ", proof ," of this fact, or more properly speaking, a meta proof . Actually, these
  13. Listed below which require choice or some weaker version thereof for their, proof ,are unprovable in ZF, but since each is provable in ZF plus the axiom of choice
  14. For a Master's degree in Arts * Arthur–Merlin protocol, an interactive, proof ,system in computational complexity theory * AM (complexity),a complexity
  15. These intangibles (objects that are proven to exist by a nonconstructive, proof , but cannot be explicitly constructed),which may conflict with some
  16. The two can be equal so their subtraction yields 0). Euclid's original, proof ,adds a third: the two lengths are not prime to one another. Euclid stipulated
  17. Only if it has no finite algebraic extension because if, within the previous, proof , the word“ algebraic” is replaced by the word“ finite ”, then the proof is
  18. S water transmitter design only after Bell's patent was granted and only as a, proof ,of concept scientific experiment to prove to his own satisfaction that
  19. Brother Nero. Caligula returned with their ashes in urns in his own hands. As, proof ,of devotion to his family, Caligula arranged the most distinguished soldiers
  20. Several results in category theory which invoke the axiom of choice for their, proof , These results might be weaker than, equivalent to, or stronger than the axiom
  21. Abstract of a completed transaction or an updated record intended to serve as a, proof ,of compliance with some administrative requirement. This is often done in
  22. A proof requiring the axiom of choice is nonconstructive: even though the, proof ,establishes the existence of an object, it may be impossible to define the
  23. Hot springs at Aachen have been channeled into baths. There is some documentary, proof ,that the Romans named the hot sulfur springs of Aachen Aquis-Granum, and indeed
  24. Some possible examples of defenses, mitigating circumstances, or failures of, proof ,are: * A defendant could argue that since he was drunk, he could not form the
  25. Greatest sin of the ancient Greek world. That was so because it not only was, proof ,of excessive pride, but also resulted in violent acts by or to those involved.
  26. The Father was seen as" the only true God ". First Corinthians - was cited as, proof ,text: A letter from Arius to the Arian Eugenics of Comedian succinctly states
  27. The axioms of field theory are“ propositions that are regarded as true without, proof , ” Rather, the field axioms are a set of constraints. If any given system of
  28. The decision whether to use of the axiom of choice (or its negation) in a, proof ,cannot be made by appeal to other axioms of set theory. The decision must be
  29. That a measure of the complexity of a program be the length of its correctness, proof , Measuring and improving the Euclid algorithms Elegance (compactness) versus
  30. Incompressible strings, the vast majority of those statements must be true. The, proof ,of this result is modeled on a self-referential construction used in Berry's
  31. Euclid stipulated this so that he could construct a reductio ad absurdum, proof ,that the two numbers' common measure is in fact the greatest. While Nicolaus
  32. We chose, the second box to the second element we chose, and so on. (A formal, proof ,for all finite sets would use the principle of mathematical induction to prove
  33. Our theory of mathematical logic since we are dealing with the very concept of, proof ,itself. Aside from this, we can also have Existential Generalization:
  34. Occasion an excuse for drinking, and he has provided posterity several quotes in, proof ,of it. Antaeus exhorts his friends to drink in celebration of a tyrant's death
  35. Whether ZF or ZFC is employed if the only question is the existence of a, proof , It is possible, however,that there is a shorter proof of a theorem from ZFC
  36. Term ended on March 4,1861. Buchanan said that the Died Scott decision was, proof ,that the South had no reason for secession, and that the Union" was intended
  37. Is modeled on a self-referential construction used in Berry's paradox. The, proof ,is by contradiction. If the theorem were false, then: Assumption (X): For any
  38. If and only if the axiom of choice holds. Nonconstructive aspects A, proof ,requiring the axiom of choice is nonconstructive: even though the proof
  39. Abandon these attempts, regarding it impossible to construct any unassailable, proof ,for the existence or non-existence of God. In his 1844 book, Philosophical
  40. Among equals. Even worse, the involvement of Marcellus provided some measure of, proof ,that Augustus’s policy was to have the youth take his place as Princes
  41. Lectures of 1934) and subsequent simplifications by Kleenex. Church's, proof ,that the Entscheidungsproblem was unsolvable, Emil Post's definition of
  42. However, the publisher had provided space for a preface in the author's, proof ,composited from the manuscript. For reasons unknown, no preface was supplied
  43. An axiom was a claim which could be seen to be true without any need for, proof , The root meaning of the word 'postulate' is to 'demand '; for instance
  44. Abraham was the one who dug the well, he also gave Abimelech seven ewes for, proof , Because of this sworn oath, they called the place of this well: Beersheba.
  45. Various sciences lay certain additional hypotheses which were accepted without, proof , Such a hypothesis was termed a postulate. While the axioms were common to many
  46. Worked out by Dr. Standoff over the next year. A grant application to build a, proof ,of concept prototype was submitted in March 1939 to the Agronomy department
  47. Admirer and mentor, Sinclair Lewis. Writing in Esquire, Lewis said," It is a, proof ,of Mr. Derleth's merit that he makes one want to make the journey and see his
  48. With:" I'll show you can't prove that a program is 'elegant'"—such a, proof ,would solve the Halting problem (ibid). Algorithm versus function computable
  49. Cannot actually computable find the complexity of arbitrary strings. This is, proof ,by contradiction where the contradiction is similar to the Berry paradox:" Let
  50. Is the existence of a proof . It is possible, however,that there is a shorter, proof ,of a theorem from ZFC than from ZF. The axiom of choice is not the only

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