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A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

A constructive proof is a proof that directly provides a specific example, or which gives an algorithm for producing an example. Constructive proofs are also called ...

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).

A proof based on a dissection which shows the formula for the area of a plane figure or of the volume of a solid. Dozens of different dissection proofs are known for the ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...

A proof by contradiction establishes the truth of a given proposition by the supposition that it is false and the subsequent drawing of a conclusion that is contradictory to ...

Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself. Instead of ...

A formal type of proof most frequently encountered in elementary geometry courses in which known or derived statements are written in the left column, and the reason that ...

A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function f(x)=ax+b (a,b in R,a!=0) is continuous at ...