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Proof and the Art of Mathematics: A Journey Through the Landscape of Mathematical Inquiry

Robert Louis Stevenson

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Published in Proof And The Art Of Mathematics: Examples And Extensions

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A proof is a logical argument that establishes the truth of a mathematical statement. A proof typically consists of a series of steps, each of which is based on a previous step or on a known fact. The final step of the proof is the statement that is being proved.

The first step in writing a proof is to identify the definitions that are relevant to the statement that is being proved. A definition is a statement that assigns a meaning to a term. For example, the definition of a "square" is "a quadrilateral with four equal sides." Once the relevant definitions have been identified, the next step is to state the axioms that will be used in the proof. An axiom is a statement that is assumed to be true without proof. For example, one of the axioms of geometry is that "two points determine a unique line."

Once the definitions and axioms have been stated, the next step is to write the proof itself. The proof should be written in a clear and concise style, and it should be easy to follow. Each step of the proof should be based on a previous step or on a known fact. The final step of the proof should be the statement that is being proved.

Proof and the Art of Mathematics: Examples and Extensions

by Joel David Hamkins

5 out of 5

Language	:	English
File size	:	5460 KB
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Print length	:	121 pages

There are many different types of proofs, but the most common types are:

The type of proof that is used to prove a statement depends on the nature of the statement. For example, direct proofs are often used to prove statements about the existence of objects, while indirect proofs are often used to prove statements about the uniqueness of objects.

Here are some tips for writing effective proofs:

Proof is the cornerstone of mathematics. The art of proof is a skill that can be developed through practice. By following the tips in this article, you can improve your ability to write effective proofs.

Proof and the Art of Mathematics: Examples and Extensions

by Joel David Hamkins

5 out of 5