A Quiz About Axiom Archimedes

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A Quiz About Axiom Archimedes

Axiom Archimedes or Archimedean property is the property of having no infinitely or infinitely small elements. It was derived from the work of Archimedes, known as the Axiom V of Archimedes, on Spheres and Cylinders. Try to ace this quiz.


Questions and Answers
  • 1. 
    Who gave the axiom of Archimedes its name because it appears as Axiom V of Archimedes on Spheres and Cylinders?
    • A. 

      Holms

    • B. 

      Otto Stolz

    • C. 

      Ostrowski

    • D. 

      Archimedes

  • 2. 
    Which of these is not a property of ordered field?
    • A. 

      It contains irrational number

    • B. 

      If x is infinitesimal its inverse is also infinite

    • C. 

      It contains rational number

    • D. 

      If x is infinitesimal and r is rational their products are also infinite

  • 3. 
    When a pair of non-zero elements is infinitesimal with respect to the other, what is it called?
    • A. 

      Strowski theorem

    • B. 

      Archimedean

    • C. 

      Non-Archimedean

    • D. 

      Heron's theorem

  • 4. 
    In which of the following is the Archimedean principle very useful?
    • A. 

      Cinematography

    • B. 

      Local field

    • C. 

      Mechanics

    • D. 

      Medicine

  • 5. 
    When was the Archimidean property named The Axiom  Archimedes?
    • A. 

      1970s

    • B. 

      1980s

    • C. 

      1880s

    • D. 

      1870s

  • 6. 
    Which of these statements is the Axiom of Archimedes?
    • A. 

      Let x be any element of K. Then there exists a rational number r such that r > x

    • B. 

      Let x be any element of K. Then there exists a natural number n such that n = x

    • C. 

      Let x be any element of K. Then there exists a natural number n such that n < x

    • D. 

      Let x be any element of K. Then there exists a natural number n such that n > x

  • 7. 
    What does K represent in Axiom of Archimedes?
    • A. 

      Ordered field

    • B. 

      Strowski determinant

    • C. 

      Axiom constant

    • D. 

      Archimedes constant

  • 8. 
    Which structure holds the Archimedean principle?
    • A. 

      Index structure

    • B. 

      Strowski Structure

    • C. 

      Algebraic structure

    • D. 

      Rational number structures

  • 9. 
    Which property must be non-Archimedean in the context of ordered field?
    • A. 

      Irrational function

    • B. 

      Rational function

    • C. 

      Real number function

    • D. 

      Strowski constant

  • 10. 
    Which of the following is not equivalent characterizations of Archimedean fields?
    • A. 

      The natural numbers are cofinal in K

    • B. 

      For any x in K the set of integers greater than x has a least element

    • C. 

      Zero is the infimum of a set

    • D. 

      Every nonempty open interval of K contains a natural number