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Maths › 00. General Mathematics ›

10.4 Common Pitfalls

10.4 Common Pitfalls Mathematical writing can fail even when the main idea is correct. The problem is often not the mathematics itself, but the way the mathematics is presented. A reader may lose the argument because a term was not defined, a step was skipped, or a symbol was used in two different ways. This section describes common mistakes and how to avoid them. Using terms before defining them A...
mathematics writing proofs style May 2, 2026
Maths › 00. General Mathematics ›

10.2 Definitions, Theorems, Proofs

10.2 Definitions, Theorems, Proofs Mathematical writing is built from a few basic parts. The most important are definitions, theorems, and proofs. A definition explains what a word or object means. A theorem states something true. A proof explains why it is true. These parts work together. A theorem uses words that must already be defined. A proof uses definitions and known facts to justify the theorem. If the definitions are...
mathematics writing definitions theorems proofs May 2, 2026
Maths › 00. General Mathematics ›

10. Writing Mathematics

Chapter 10. Writing Mathematics Mathematics is written so that ideas can be checked, reused, and understood by other people. A correct idea may still be hard to follow if it is written poorly. Good mathematical writing makes the structure visible. This chapter introduces the basic craft of writing mathematics. It explains how to organize a mathematical text, how to state definitions and theorems, how to write proofs, and how to...
mathematics writing communication proofs May 2, 2026
Maths › 00. General Mathematics ›

01.5 Constructive vs Classical Viewpoints

1.5 Constructive vs Classical Viewpoints Mathematics has more than one standard way to interpret proof. The two most important viewpoints are classical and constructive mathematics. Classical mathematics accepts the usual laws of logic, including the law of excluded middle: P or not P For any proposition P , classical logic says that either P is true or P is false. This principle allows indirect proofs. To prove that an object...
mathematics foundations constructivism classical-logic proofs May 2, 2026