Equivalence Relation
An equivalence relation on a set 
is a Subset of 
, i.e., a collection 
of ordered pairs of elements of, satisfying certain properties. Write ``
'' to mean 
is an element of , and we say ``
is related to
,'' then the properties are
- 1. Reflexive:
for all 
, - 2. Symmetric:
Implies 
for all 
- 3. Transitive: and
imply 
for all 
,
or 
.See also Equivalence Class, Teichmüller Space
References
Stewart, I. and Tall, D. The Foundations of Mathematics. Oxford, England: Oxford University Press, 1977.
- Astroid
- Astroidal Ellipsoid
- Astroid Evolute
- Astroid Involute
- Astroid Pedal Curve
- Astroid Radial Curve
- Asymptosy
- Asymptote
- Asymptotic
- Asymptotic Curve
- Asymptotic Direction
- Asymptotic Notation
- Asymptotic Series
- Atiyah-Singer Index Theorem
- Atkin-Goldwasser-Kilian-Morain Certificate
- Atomic Statement
- Attraction Basin
- Attractor
- Auction
- Augend
- Augmented Amicable Pair
- Augmented Dodecahedron
- Augmented Hexagonal Prism
- Augmented Pentagonal Prism
- Augmented Polyhedron