Mathematics Quiz

Number theory = Properties of numbers and their relationships Algebra = Formulas and related structures Geometry = Shapes and the spaces in which they are contained Analysis = Quantities and their changes

Abstract objects = Entities with stipulated properties called axioms Deductive rules = Succession of applications to established results Theorems = Previously proved results Axioms = Basic properties considered true starting points of a theory

Most mathematical activity involves discovery of properties of abstract objects = Pure reason is used to prove properties of abstract objects Modern mathematics includes entities stipulated to have certain properties = Abstract objects consist of either abstractions from nature or stipulated entities A proof consists of a succession of applications of deductive rules = A proof involves applying deductive rules to established results Abstraction from nature involves some basic properties considered true starting points of the theory = Some basic properties are considered true starting points in abstraction from nature

<p>Mathematical activity = Involves discovery of properties and use of pure reason Proof = Succession of applications of deductive rules Abstract objects = Either abstractions from nature or stipulated entities Axioms = Properties considered true starting points of a theory</p> Signup and view all the answers

<p>Discovery of properties of abstract objects = Main activity in modern mathematics Use of pure reason to prove properties = Common method in mathematical activity Entities stipulated to have certain properties = Representation of abstract objects in modern mathematics Succession of applications of deductive rules = Process of creating a proof in mathematics</p> Signup and view all the answers

<p>Number theory, algebra, geometry, and analysis</p> Signup and view all the answers

<p>The discovery of properties of abstract objects and the use of pure reason to prove them</p> Signup and view all the answers

<p>A succession of applications of deductive rules to already established results</p> Signup and view all the answers

<p>Abstractions from nature or entities stipulated to have certain properties, called axioms</p> Signup and view all the answers

<p>Axioms and, in case of abstraction from nature, some basic properties</p> Signup and view all the answers

<p>Numbers, formulas, structures, shapes, and quantities</p> Signup and view all the answers

<p>Number theory, algebra, geometry, and analysis</p> Signup and view all the answers

<p>Discovery of properties of abstract objects and use of pure reason to prove them</p> Signup and view all the answers

<p>A succession of applications of deductive rules to already established results</p> Signup and view all the answers

<p>Abstractions from nature or stipulated entities with certain properties called axioms</p> Signup and view all the answers