Test Your Knowledge About Existence Theorems

10 Questions | Total Attempts: 108

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Test Your Knowledge About Existence Theorems - Quiz

Existence theorems regroup any mathematical or scientific statement beginning with "there exists. . . ", or "for all x,y there exists. . . ", etc. In other words, it is a theorem with a prenex normal form involving the existential quantifier. Do you want to take a chance and pass our quiz about this type of theorem? Try it and see how well you do.


Questions and Answers
  • 1. 
    What is constructive mathematics?
    • A. 

      It is the continuity of a function such as a sin x proven as a constructive bound on the modulus of continuity

    • B. 

      It is the stagnation of a function such as a sin x proven as a constructive bound on the modulus of continuity

    • C. 

      It is the improvement of a function such as a sin x proven as a constructive bound on the modulus of continuity

    • D. 

      It is the continuity of a function such as a tan x proven as a constructive bound on the modulus of continuity

  • 2. 
    What is the axiom of infinity?
    • A. 

      It's a very complicated rule.

    • B. 

      It's the principle behind plus and minus infinity.

    • C. 

      It is 1 of the axioms of Zermelo-Fraenkel set theory.

    • D. 

      It is 1 of the axioms of the Newton set theory.

  • 3. 
    What is an existential quantification?
    • A. 

      It's a type of function, which is interpreted as "there exists"; "there is at least one", etc.

    • B. 

      It's what led to the discovery of the number "0"

    • C. 

      It's what helps us give value to numbers.

    • D. 

      It's a type of quantifier, a logical constant which is interpreted as "there exists"; "there is at least one", etc.

  • 4. 
    What is a big O notation?
    • A. 

      It's a mathematical notation describing the limiting behavior of a function when the argument tends towards a particular value of infinity.

    • B. 

      It's a theorem which defines the circumference of earth.

    • C. 

      It is a rule which defines the circumference of earth.

    • D. 

      It is the great rule that helped navigators during the 15th Century.

  • 5. 
    What is a sine?
    • A. 

      It's the trigonometric function of an angle.

    • B. 

      It's the third side of a triangle.

    • C. 

      It's the degree of an angle.

    • D. 

      It's a rule in geometry.

  • 6. 
    What is the law of excluded middle?
    • A. 

      It's the portion of solution which includes number from 0 to + infinity.

    • B. 

      It's a law which states that for any proposition, either that a proposition is true or that its negation is true.

    • C. 

      It's the perfect half.

    • D. 

      It's the median of a function.

  • 7. 
    What is an axiom of choice?
    • A. 

      It is an axiom of set of theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is empty.

    • B. 

      It is an axiom of set of theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.

    • C. 

      It is an axiom of set of theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is solvable.

    • D. 

      It is an axiom of set of theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is superior to 1.

  • 8. 
    How is an axiom of choice also called?
    • A. 

      CA

    • B. 

      AC.

    • C. 

      AB

    • D. 

      AX

  • 9. 
    What is a first-order logic?
    • A. 

      It's a collection of formal systems used in math, philosophy, linguistics, and computer science.

    • B. 

      It's a collection of formal systems used in math, philosophy, and computer science.

    • C. 

      It's a collection of formal systems used in math and computer science.

    • D. 

      It's a collection of formal systems used in math, philosophy, and computer science.

  • 10. 
    What is a numerical analysis?
    • A. 

      It is a study of algorithms that use numerical approximation for the problems of mathematical analysis.

    • B. 

      It is a study of theorems that use numerical approximation for the problems of mathematical analysis.

    • C. 

      It is a study of algorithms that use statistical approximation for the problems of mathematical analysis.

    • D. 

      It is a study of algorithms that use symbols for the problems of mathematical analysis.

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