A Quiz About Axiom Archimedes

10 Questions | Total Attempts: 130

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A Quiz About Axiom Archimedes - Quiz

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

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