Concept
Reflexive relation
Overview
In mathematics, a binary relation
R
{\displaystyle R}
on a set
X
{\displaystyle X}
is reflexive if it relates every element of
X
{\displaystyle X}
to itself.
An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Any kind of dissimilarity is also of this kind: if the colour of A is unlike the colour of B, then the colour of B is unlike the colour of A. Relations of this sort are called _symmetrical_. Thus a relation is symmetrical if, whenever it holds between A and B, it also holds between B and A. All relations that are not symmetrical are called _non-symmetrical_. Thus "brother" is non-symmetrical, because, if A is a…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
States what Reflexive relation is; the author is tied to Reflexive relation in the knowledge graph.
Two sets of four points each are defined as having the same anharmonic ratio, when (1) each set of four lies in one straight line, and (2) corresponding points of different sets lie two by two on four straight lines through a single point, or when both sets have this relation to any third set[123]. And reciprocally: Two sets of four straight lines are defined as having the same anharmonic ratio when (1) each set of…
Bertrand Russell, An essay on the foundations of geometry
States what Reflexive relation is; the author is tied to Reflexive relation in the knowledge graph.
When we think of mathematics, we have in our mind a science devoted to the exploration of number, quantity, geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical relations. The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities.
Alfred North Whitehead, Science and the modern world
Close in meaning to Reflexive relation; the term itself is not named.
Philosophers who discussed Reflexive relation
Related ideas
- Giuseppe Peano
- Parity (mathematics)
- Integer
- If and only if
- Mathematics
- Real number
- Natural number
- Oxford English Dictionary
- Set (mathematics)
- Subset
- Philosophical logic
- Bertrand Russell
- Medieval Latin
- Equivalence relation
Opposing perspectives
Place in the tradition
Part of Epistemic modal logic.