Math 2.0

General and overarching topics Concept

Mathematical proof

Builds on Modus ponens

Summary

A mathematical proof is an argument that shows that a statement follows from axioms, definitions and statements that are already proved. Each step of a proof follows from earlier steps by a valid rule of inference, such as modus ponens. A proved statement is a theorem.

Remarks

Common methods are direct proof, proof by contrapositive, proof by contradiction and proof by cases. A formal proof is a sequence of formulas in a formal system. A computer can check it, for example in Lean. Examples, however many, do not prove a universal statement.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Proposition, concept, no evidence levelPropositionconceptImplication, definition, no evidence levelImplicationdefinitionModus ponens, concept, no evidence levelModus ponensconceptMathematical proof, concept, no evidence levelMathematical proofconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proposition concept
  2. Implication definition
  3. Modus ponens concept
  4. Mathematical proof concept

Where this leads

44 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Mathematical_proof, lead section
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Aliasesproof
Kindconcept
WritingW1 stated
MSC00A35
UsesModus ponens
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  • edge not_instance_of in: at least one non-example (0 of 1)

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