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What are the major subdisciplines of modern mathematics mentioned in the text?
What are the major subdisciplines of modern mathematics mentioned in the text?
- Arithmetic, calculus, algebra, and statistics
- Geometry, topology, number theory, and calculus
- Number theory, algebra, geometry, and analysis (correct)
- Calculus, statistics, trigonometry, and topology
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?
- Trial and error with iterative refinement
- Empirical observation and experimental verification
- Discovery of properties of abstract objects and use of pure reason to prove them (correct)
- Inductive reasoning and intuitive understanding
What do mathematical proofs consist of, according to the text?
What do mathematical proofs consist of, according to the text?
- A combination of deductive and inductive reasoning
- A series of experimental tests and observations
- A succession of applications of deductive rules to already established results (correct)
- A process of trial and error to validate conjectures
What are the objects that mathematical proofs are based on, as mentioned in the text?
What are the objects that mathematical proofs are based on, as mentioned in the text?
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What is the nature of the general consensus among mathematicians about a common definition for their academic discipline, as per the text?
What is the nature of the general consensus among mathematicians about a common definition for their academic discipline, as per the text?
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What are the major subdisciplines of modern mathematics?
What are the major subdisciplines of modern mathematics?
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What is the primary method used in mathematical activity?
What is the primary method used in mathematical activity?
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What do proofs in mathematics consist of?
What do proofs in mathematics consist of?
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What are the objects that mathematical proofs consist of?
What are the objects that mathematical proofs consist of?
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What is the nature of most mathematical objects in modern mathematics?
What is the nature of most mathematical objects in modern mathematics?
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