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  2. Constructive proof - Wikipedia

    en.wikipedia.org/wiki/Constructive_proof

    In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem ), which proves the existence of a particular kind of object ...

  3. Constructivism (philosophy of mathematics) - Wikipedia

    en.wikipedia.org/wiki/Constructivism_(philosophy...

    In classical real analysis, one way to define a real number is as an equivalence class of Cauchy sequences of rational numbers.. In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ(n), together with a function g that takes a positive integer n and outputs a positive integer g(n) such that

  4. Intuitionistic logic - Wikipedia

    en.wikipedia.org/wiki/Intuitionistic_logic

    Many tautologies in classical logic are not theorems in intuitionistic logic – in particular, as said above, one of intuitionistic logic's chief aims is to not affirm the law of the excluded middle so as to vitiate the use of non-constructive proof by contradiction, which can be used to furnish existence claims without providing explicit ...

  5. Intuitionism - Wikipedia

    en.wikipedia.org/wiki/Intuitionism

    The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that ...

  6. Existence theorem - Wikipedia

    en.wikipedia.org/wiki/Existence_theorem

    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 ...

  7. The 10 Hardest Restaurant Reservations to Book in America - AOL

    www.aol.com/10-hardest-restaurant-reservations...

    Rao’s. New York. With no shortage of hard-to-book eateries, Rao’s stands out.Open since 1896, 60 percent of the tables are reserved for regulars who have standing reservations. To dine here ...

  8. Type theory - Wikipedia

    en.wikipedia.org/wiki/Type_theory

    Constructive mathematics requires when proving "there exists an with property ()", one must construct a particular and a proof that it has property . In type theory, existence is accomplished using the dependent product type, and its proof requires a term of that type. An example of a non-constructive proof is proof by contradiction.

  9. Drinking coffee at a certain time of day could reduce death ...

    www.aol.com/drinking-coffee-certain-time-day...

    "Moderate coffee drinking has been related to health benefits," lead study author Lu Qi, M.D., PhD, interim chair of the Department of Epidemiology at Tulane University, told Fox News Digital.

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