reflexivity
logic and mathematics
Also known as: reflexive law, reflexive relation
Quick Summary
In logic and mathematics, a relation is a set of ordered pairs, triples, or n-tuples. Key properties of relations include symmetry, transitivity, and reflexivity.1
- Reflexivity means a relation holds between an object and itself. For example, "x is at least as tall as y" is reflexive because any object is at least as tall as itself.1
- Symmetry occurs when if a relation holds between x and y, it also holds between y and x, like "x is parallel to y".1
- Transitivity means if a relation holds between x and y, and between y and z, it also holds between x and z, such as "x is greater than y".1
Relations that are reflexive, symmetric, and transitive are called equivalence relations. These concepts are fundamental in set theory and formal logic. Paradoxes can arise when self-referential statements are made about relations, such as the liar paradox.23456
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