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  2. Consistent and inconsistent equations - Wikipedia

    en.wikipedia.org/wiki/Consistent_and...

    In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.

  3. Consistency - Wikipedia

    en.wikipedia.org/wiki/Consistency

    Such a theory is consistent if and only if it does not prove a particular sentence, called the Gödel sentence of the theory, which is a formalized statement of the claim that the theory is indeed consistent. Thus the consistency of a sufficiently strong, recursively enumerable, consistent theory of arithmetic can never be proven in that system ...

  4. Consistency (statistics) - Wikipedia

    en.wikipedia.org/wiki/Consistency_(statistics)

    A consistent estimator is one for which, when the estimate is considered as a random variable indexed by the number n of items in the data set, as n increases the estimates converge in probability to the value that the estimator is designed to estimate.

  5. Consistent estimator - Wikipedia

    en.wikipedia.org/wiki/Consistent_estimator

    In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter θ 0 —having the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probability to θ 0.

  6. Theory (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Theory_(mathematical_logic)

    A syntactically consistent theory is a theory from which not every sentence in the underlying language can be proven (with respect to some deductive system, which is usually clear from context). In a deductive system (such as first-order logic) that satisfies the principle of explosion , this is equivalent to requiring that there is no sentence ...

  7. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]

  8. Some critics of Janssen, including plaintiff’s lawyers, have ...

    highline.huffingtonpost.com/miracleindustry/...

    4 ! adolescents ages 13 to 17 and for the short-term treatment of manic or mixed episodes of bipolar I disorder in children and adolescents ages 10 to 17.4 o In approving Risperdal for the irritability associated with autistic disorders in

  9. Complete theory - Wikipedia

    en.wikipedia.org/wiki/Complete_theory

    In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation is provable. That is, for every sentence φ , {\displaystyle \varphi ,} the theory T {\displaystyle T} contains the sentence or its negation but not both (that is, either T ⊢ φ ...