Test Your Knowledge About Existence Theorems

1) What is an existential quantification?

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

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

It's what helps us give value to numbers.

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

The correct answer explains that existential quantification is a type of quantifier in logic. It is a logical constant that is interpreted as "there exists" or "there is at least one". This means that it is used to express the existence of at least one object that satisfies a given condition.

Explanation

The correct answer explains that existential quantification is a type of quantifier in logic. It is a logical constant that is interpreted as "there exists" or "there is at least one". This means that it is used to express the existence of at least one object that satisfies a given condition.

2) What is a sine?

It's the trigonometric function of an angle.

It's the third side of a triangle.

It's the degree of an angle.

It's a rule in geometry.

The correct answer is "It's the trigonometric function of an angle." In trigonometry, a sine is a mathematical function that relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. It is commonly denoted as sin and is used to calculate angles and sides in various mathematical and scientific applications.

Explanation

The correct answer is "It's the trigonometric function of an angle." In trigonometry, a sine is a mathematical function that relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. It is commonly denoted as sin and is used to calculate angles and sides in various mathematical and scientific applications.

3) What is constructive mathematics?

not-available-via-ai

Explanation

not-available-via-ai

4) What is a big O notation?

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

It is a rule which defines the circumference of earth.

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

not-available-via-ai

Explanation

not-available-via-ai

5) What is the law of excluded middle?

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

It's the perfect half.

It's the median of a function.

The law of excluded middle states that for any proposition, it is either true or its negation is true. This means that there is no middle ground or alternative possibility - a proposition cannot be both true and not true at the same time. This principle is fundamental in classical logic and is often used as a basis for reasoning and proof. It allows for clear and binary distinctions between truth values, simplifying logical analysis and decision-making processes.

Explanation

The law of excluded middle states that for any proposition, it is either true or its negation is true. This means that there is no middle ground or alternative possibility - a proposition cannot be both true and not true at the same time. This principle is fundamental in classical logic and is often used as a basis for reasoning and proof. It allows for clear and binary distinctions between truth values, simplifying logical analysis and decision-making processes.

6) What is an axiom of choice?

The correct answer is that the axiom of choice is equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty. This means that for any collection of sets, each containing at least one element, it is possible to choose one element from each set to form a new set. This axiom is an important tool in mathematics and has applications in various areas such as analysis, topology, and algebra. It allows for the construction of certain mathematical objects that would otherwise be impossible to define.

Explanation

The correct answer is that the axiom of choice is equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty. This means that for any collection of sets, each containing at least one element, it is possible to choose one element from each set to form a new set. This axiom is an important tool in mathematics and has applications in various areas such as analysis, topology, and algebra. It allows for the construction of certain mathematical objects that would otherwise be impossible to define.

7) How is an axiom of choice also called?

CA

AC.

AB

AX

An axiom of choice is also known as AC.

Explanation

An axiom of choice is also known as AC.

8) What is a first-order logic?

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

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

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

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

The correct answer is "It's a collection of formal systems used in math, philosophy, linguistics, and computer science." This answer encompasses all the disciplines mentioned in the question and accurately describes the scope of first-order logic.

Explanation

The correct answer is "It's a collection of formal systems used in math, philosophy, linguistics, and computer science." This answer encompasses all the disciplines mentioned in the question and accurately describes the scope of first-order logic.

9) What is the axiom of infinity?

It's a very complicated rule.

It's the principle behind plus and minus infinity.

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

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

The axiom of infinity is one of the axioms of Zermelo-Fraenkel set theory. This axiom states that there exists at least one set, denoted as "omega," that contains the empty set and is closed under the successor function. In other words, it guarantees the existence of an infinite set in the theory. This axiom is fundamental in establishing the existence of infinite sets and is widely accepted in modern set theory.

Explanation

The axiom of infinity is one of the axioms of Zermelo-Fraenkel set theory. This axiom states that there exists at least one set, denoted as "omega," that contains the empty set and is closed under the successor function. In other words, it guarantees the existence of an infinite set in the theory. This axiom is fundamental in establishing the existence of infinite sets and is widely accepted in modern set theory.

10) What is a numerical analysis?

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

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

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

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

Numerical analysis is a field of study that focuses on developing and analyzing algorithms that involve numerical approximation to solve problems in mathematical analysis. This involves using numerical methods and techniques to approximate solutions to mathematical problems, such as finding roots of equations, solving differential equations, and evaluating integrals. By using numerical approximation, these algorithms provide efficient and practical solutions to complex mathematical problems that may not have exact analytical solutions.

Explanation

Numerical analysis is a field of study that focuses on developing and analyzing algorithms that involve numerical approximation to solve problems in mathematical analysis. This involves using numerical methods and techniques to approximate solutions to mathematical problems, such as finding roots of equations, solving differential equations, and evaluating integrals. By using numerical approximation, these algorithms provide efficient and practical solutions to complex mathematical problems that may not have exact analytical solutions.