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