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Explain the major subdisciplines of modern mathematics as represented in the text.
Explain the major subdisciplines of modern mathematics as represented in the text.
The major subdisciplines of modern mathematics are number theory, algebra, geometry, and analysis.
What does mathematical activity primarily involve, according to the text?
What does mathematical activity primarily involve, according to the text?
Mathematical activity primarily involves the discovery of properties of abstract objects and the use of pure reason to prove them.
Define what a proof consists of in mathematics, as described in the text.
Define what a proof consists of in mathematics, as described in the text.
A proof consists of a succession of applications of deductive rules to already established results, including previously proved theorems, axioms, and basic properties.
What are the entities in modern mathematics stipulated to have certain properties called?
What are the entities in modern mathematics stipulated to have certain properties called?
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What is the lack of general consensus among mathematicians about, as mentioned in the text?
What is the lack of general consensus among mathematicians about, as mentioned in the text?
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