Questions and Answers
Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature or—in modern mathematics—entities that are stipulated to have certain ______, called axioms.
properties
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related ______, shapes and the spaces in which they are contained, and quantities and their changes.
structures
A proof consists of a succession of applications of deductive rules to already established ______.
results
There is no general consensus among mathematicians about a common definition for their academic ______.
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These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and ______, respectively.
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