Math 2.0

Mathematical logic and foundations Definition

Converse relation

Builds on Binary relation

Definition

Let R⊆A×BR \subseteq A \times B be a binary relation from AA to BB. The converse of RR is the relation from BB to AA R−1={(b,a)∈B×A∣(a,b)∈R}.R^{-1} = \{(b, a) \in B \times A \mid (a, b) \in R\}. So bR−1ab \mathrel{R^{-1}} a if and only if aRba \mathrel{R} b.

Remarks

Other names are the inverse relation and the transpose. Another notation is RTR^{T}. The converse of << on ℝ\mathbb{R} is >>. The converse of the converse of RR is RR. For a bijection ff, the converse of the graph of ff is the graph of the inverse function.

Reading path

To understand this page from the ground up, read these 11 pages in order. The foundations come first.

Show the path as a graph
Element, definition, no evidence levelElementdefinitionProposition, concept, no evidence levelPropositionconceptSet, definition, no evidence levelSetdefinitionImplication, definition, no evidence levelImplicationdefinitionPredicate, definition, no evidence levelPredicatedefinitionOrdered pair, definition, no evidence levelOrdered pairdefinitionUniversal quantifier, definition, no evidence levelUniversal quantifierdefinitionCartesian product, definition, no evidence levelCartesian productdefinitionSubset, definition, no evidence levelSubsetdefinitionBinary relation, definition, no evidence levelBinary relationdefinitionConverse relation, definition, no evidence levelConverse relationdefinition
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. Element definition
  2. Proposition concept
  3. Set definition
  4. Implication definition
  5. Predicate definition
  6. Ordered pair definition
  7. Universal quantifier definition
  8. Cartesian product definition
  9. Subset definition
  10. Binary relation definition
  11. Converse relation definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Converse_relation, lead section
About this page
Tag0JCSQNNP2M
URIm2://0JCSQNNP2M
Kinddefinition
WritingW0 stub
MSC03E20
DefinesConverse relation
UsesBinary relation

Markdown · JSON · Edit on GitHub

What this page 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 page is. They do not measure its truth.

What links here

No page links to this page yet.