Mastering Mathematics
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Questions and Answers

Name the major subdisciplines of modern mathematics.

Number theory, algebra, geometry, and analysis.

What is the main focus of mathematical activity?

The discovery of properties of abstract objects and the use of pure reason to prove them.

What are the two types of objects in modern mathematics?

Abstractions from nature and entities that are stipulated to have certain properties.

What does a proof consist of?

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

What are the three types of results used in a proof?

<p>Previously proved theorems, axioms, and abstractions from nature or stipulated entities with certain properties.</p> Signup and view all the answers

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