Math 2.0

topic

Proof methods

Summary

This topic collects the standard methods of mathematical proof, such as direct proof, proof by contradiction, proof by cases and induction. A proof node names its methods with the method edge, and each target of that edge is a concept in this topic. The topic lets a reader find all the proofs that use one method.

What this node needs for W1
  • an inventory row: the row of the inventory that the node accounts for (0 of 1)

The writing levels say how complete the text of a node is. They do not measure its truth.

Blueprint

The members of this topic and each node that they need, 25 nodes in all. A member has a thick border in the figure and the mark "member" in the list.

Cantor's diagonal argument, concept, no evidence levelCantor's diagonal arg…conceptDouble counting, concept, no evidence levelDouble countingconceptMathematical induction, concept, no evidence levelMathematical inductionconceptProof by infinite descent, concept, no evidence levelProof by infinite des…conceptProposition, concept, no evidence levelPropositionconceptConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionPredicate, definition, no evidence levelPredicatedefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionTruth table, concept, no evidence levelTruth tableconceptModus ponens, concept, no evidence levelModus ponensconceptExistential quantifier, definition, no evidence levelExistential quantifierdefinitionPropositional logic, concept, no evidence levelPropositional logicconceptMathematical proof, concept, no evidence levelMathematical proofconceptTautology, definition, no evidence levelTautologydefinitionProof by cases, concept, no evidence levelProof by casesconceptDirect proof, concept, no evidence levelDirect proofconceptConstructive proof, concept, no evidence levelConstructive proofconceptLogical equivalence, definition, no evidence levelLogical equivalencedefinitionDouble negation law, statement, no evidence levelDouble negation lawstatementContrapositive, statement, no evidence levelContrapositivestatementProof by contradiction, concept, no evidence levelProof by contradictionconceptProof by contrapositive, concept, no evidence levelProof by contrapositi…concept
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Cantor's diagonal argument concept member
  2. Double counting concept member
  3. Mathematical induction concept member
  4. Proof by infinite descent concept member
  5. Proposition concept
  6. Conjunction definition
  7. Disjunction definition
  8. Implication definition
  9. Negation definition
  10. Predicate definition
  11. Biconditional definition
  12. Truth table concept
  13. Modus ponens concept
  14. Existential quantifier definition
  15. Propositional logic concept
  16. Mathematical proof concept
  17. Tautology definition
  18. Proof by cases concept member
  19. Direct proof concept member
  20. Constructive proof concept member
  21. Logical equivalence definition
  22. Double negation law statement
  23. Contrapositive statement
  24. Proof by contradiction concept member
  25. Proof by contrapositive concept member

Sources

  1. Web https://en.wikipedia.org/wiki/Mathematical_proof, Methods of proof

What links here

Nodes in this topic