Mathematical logic and foundations Definition
Symmetric relation
Builds on Binary relation
Definition
Let be a binary relation on a set . The relation is symmetric when, for all , implies .
Remarks
Equality is symmetric. The relation on is not symmetric, because but not . A relation is symmetric exactly when it is equal to its converse.
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
- no evidence level
- Element definition
- Proposition concept
- Set definition
- Implication definition
- Predicate definition
- Ordered pair definition
- Universal quantifier definition
- Cartesian product definition
- Subset definition
- Binary relation definition
- Symmetric relation definition
Where this leads
67 pages build on this one.
- A finite group is nilpotent iff it is the product of its Sylow subgroups
- Equivalence classes form a partition
- Torus
- Möbius strip
- Groups of prime order are cyclic
- Correspondence between equivalence relations and partitions
- Equivalence class
- Order of an element divides the order of the group
- Fixed points of a p-group action
- Second Sylow theorem
- Groups of order p squared are abelian
- The number of Sylow subgroups is the index of the normaliser
- Universal property of the quotient topology
- The alternating group A5 is simple
- Abelian simple groups have prime order
- Cauchy's theorem
- The number of Sylow subgroups divides the index
- Converse of Lagrange's theorem fails for the alternating group A4
- Third Sylow theorem
- Equivalence relation induced by a function
- Frattini argument
- Size of an orbit times the size of the stabiliser
- Path component
- Equivalence relation
- Quotient topology
- First Sylow theorem
- Circle as a quotient of the real line
- Groups of order pq
- Burnside's lemma
- g to the order of the group is the identity
- Quotient set
- Relative CW complex
- Translation surface
- Weak ordering
- Discrete series representation
- Classification of surfaces
- Lagrange's theorem
- Oscillator representation
- Kolmogorov–Arnold–Moser theorem
- Galois group of a prime degree polynomial with two nonreal roots
- Lp space
- Nichols–Zoeller theorem
- Standard map
- Hall's theorem on solvable groups
- Proof that the order of an element divides the order of the group
- Arnold's cat map
- Integral operator
- Hall subgroup
- Sylow theorems
- Frattini subgroup
- Proof that groups of prime order are cyclic
- Action-angle coordinates
- Sinai billiard
- Milnor's isospectral flat tori
- Orbifold
- Torus knot
- Orientation of a manifold
- Real projective plane
- Liouville–Arnold theorem
- Proof of Lagrange's theorem
- Pseudo-Anosov map
- Geometric realization
- Torus as a group
- Bunimovich stadium
- Maximal torus
- Symmetric and self-reciprocal kernels
- Stone–von Neumann theorem
Further reading
- Web https://en.wikipedia.org/wiki/Symmetric_relation, lead section
About this page
| Tag | 0N9SA25Z3V |
|---|---|
| URI | m2://0N9SA25Z3V |
| Kind | definition |
| Writing | W1 stated |
| MSC | 03E20 |
| Defines | Symmetric relation |
| Uses | Binary relation |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge instance_of in: one example (0 of 1)
- edge not_instance_of in: one non-example that fails one clause (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.