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Questions and Answers
What are the major subdisciplines of modern mathematics mentioned in the text?
What are the major subdisciplines of modern mathematics mentioned in the text?
- Number theory, algebra, geometry, and analysis (correct)
- Logic, topology, calculus, and algebra
- Arithmetic, statistics, topology, and calculus
- Calculus, statistics, trigonometry, and arithmetic
What is the primary method used in mathematical activity, as per the text?
What is the primary method used in mathematical activity, as per the text?
- Observation of natural phenomena and experimental testing
- Intuition and guesswork
- Trial and error
- Discovery of properties of abstract objects and use of pure reason to prove them (correct)
What do proofs in mathematics consist of, based on the text?
What do proofs in mathematics consist of, based on the text?
- A series of educated guesses
- A collection of experimental data
- A summary of popular beliefs
- A succession of applications of deductive rules to already established results (correct)
What are the objects that mathematical proofs involve, according to the text?
What are the objects that mathematical proofs involve, according to the text?
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What is the nature of the general consensus among mathematicians regarding the definition of mathematics, as per the text?
What is the nature of the general consensus among mathematicians regarding the definition of mathematics, as per the text?
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