Criterion

A Criterion is a condition that set of conditions that must hold for a result to be true.

• AKA: Criterium, Mathematical Criterion.
• Context:
  • It can be a theorem.
  • It can range from being Sufficient Condition, to being a Necessary Condition, to being a Necessary and Sufficient Condition.
  • …
• Example(s)
  • Abel criterion.
  • Brown's Criterion
  • Cauchy Criterion.
  • D'Alembert Criterion.
  • Dirichlet Criterion.
  • Dini-Lipschitz Criterion.
  • Divisibility Criterion.
  • Du Bois-Reymond Criterion.
  • Eisenstein's Criterion.
  • Euler's Criterion
  • Euler-MacLaurin Criterion.
  • Gauss's Criterion.
  • Hardy criterion.
  • Korselt's Criterion.
  • Kummer Criterion.
  • Leibniz Criterion.
  • Lienard-Chipart Criterion.
  • Logarithmic Convergence Criterion.
  • Luzin criterion.
  • Maximin Criterion.
  • Mikhailov Criterion.
  • Nyquist criterion.
  • Pocklington's Criterion.
  • Raabe Criterion.
  • Routh-Hurwitz Criterion.
  • Vandiver's Criteria.
  • Weyl's Criterion.
• Counter-Example(s)
  • Hypothesis.
  • Axiom.
• See: Optimality Criterion, Multi-Criterion Problem.

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References

2017a

• (Weisstein, 2017) ⇒ Retrieved on 2017-05-21 from Weisstein, Eric W. “Criterion." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/Criterion.html
  • A requirement necessary for a given statement or theorem to hold. Also called a condition.

2017b

• (Wikipedia, 2017) ⇒ Retrieved on 2017-05-07 from http://en.wikipedia.org/wiki/Criterion#Science_and_mathematics
• Criterion validity, in psychometrics, a measure of how well one variable or set of variables predicts an outcome
• Criterion-referenced test, translates a test score into a statement about the behavior to be expected of a person
• Eisenstein's criterion, in mathematics, gives sufficient conditions for a polynomial to be irreducible over the rational numbers
• Euler's criterion, in number theory concerning primes
• Problem of the criterion, in epistemology, an issue regarding the starting point of knowledge
• Weyl's criterion, used in mathematics in the theory of diophantine approximation.

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