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Mathematics is an area of knowledge that includes the topics of ______, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes.
Mathematics is an area of knowledge that includes the topics of ______, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes.
numbers
These topics are represented in modern mathematics with the major subdisciplines of number theory, ______, geometry, and analysis, respectively.
These topics are represented in modern mathematics with the major subdisciplines of number theory, ______, geometry, and analysis, respectively.
algebra
There is no general consensus among mathematicians about a common definition for their academic ______.
There is no general consensus among mathematicians about a common definition for their academic ______.
discipline
Most mathematical activity involves the discovery of properties of ______ objects and the use of pure reason to prove them.
Most mathematical activity involves the discovery of properties of ______ objects and the use of pure reason to prove them.
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A proof consists of a succession of applications of ______ rules to already established results.
A proof consists of a succession of applications of ______ rules to already established results.
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