A Quiz About Axiom Archimedes

10 Questions | By Gregorynaomi | Updated: Mar 18, 2022 | Attempts: 166

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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