10 Questions

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