Mathematics: Fundamentals and Subdisciplines

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What are the major subdisciplines of modern mathematics?

Calculus, statistics, trigonometry, topology

Number theory, geometry, algebra, analysis (correct)

Arithmetic, calculus, differential equations, probability

Algebra, geometry, calculus, topology

What is the primary method used in mathematical activity?

Trial and error experimentation with physical objects

Use of inductive reasoning to make generalizations

Discovery of properties of abstract objects and use of pure reason to prove them (correct)

Relying on empirical evidence to draw conclusions

How are proofs constructed in mathematics?

Succession of applications of deductive rules to already established results (correct)

Application of trial and error to find the correct result

Reliance on intuition and guesswork

Random selection of axioms and theorems

In which fields is mathematics essential?

Natural sciences, engineering, medicine, finance, computer science Signup and view all the answers

Are the fundamental truths of mathematics dependent on scientific experimentation?

No, they are independent from any scientific experimentation Signup and view all the answers

What is the term for a definition that lists the objects that a term describes?

Extensional definition Signup and view all the answers

In mathematics, what is the purpose of a definition?

To describe a condition that qualifies what a mathematical term is and is not Signup and view all the answers

What is the term for the word or group of words that is to be defined?

Definiendum Signup and view all the answers

Which category of definitions conveys the meaning of a term by pointing out examples?

Ostensive definitions Signup and view all the answers

What is the basis on which all of modern mathematics is constructed?

Definitions Signup and view all the answers

What is the term for the word or group of words that is to be defined?

Definiendum Signup and view all the answers

Which category of definitions conveys the meaning of a term by pointing out examples?

Ostensive Signup and view all the answers

What is the term for a definition that lists the objects that a term describes?

Extensional Signup and view all the answers

In the definition 'An elephant is a large gray animal native to Asia and Africa', what is the definiens?

Large gray animal Signup and view all the answers

What is the basis on which all of modern mathematics is constructed?

Definitions and axioms Signup and view all the answers

Mathematics: Fundamentals and Subdisciplines

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Questions and Answers

What are the major subdisciplines of modern mathematics?

What is the primary method used in mathematical activity?

How are proofs constructed in mathematics?

In which fields is mathematics essential?

Are the fundamental truths of mathematics dependent on scientific experimentation?

What is the term for a definition that lists the objects that a term describes?

In mathematics, what is the purpose of a definition?

What is the term for the word or group of words that is to be defined?

Which category of definitions conveys the meaning of a term by pointing out examples?

What is the basis on which all of modern mathematics is constructed?

What is the term for the word or group of words that is to be defined?

Which category of definitions conveys the meaning of a term by pointing out examples?

What is the term for a definition that lists the objects that a term describes?

In the definition 'An elephant is a large gray animal native to Asia and Africa', what is the definiens?

What is the basis on which all of modern mathematics is constructed?

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